Question: What city is the county seat of Barber County and is 4 miles southeast of the community of Pixley?

Context articles: New Somerset, Ohio
Goshen, Indiana
Barber County, Kansas
Wirock, Minnesota
Gibson Generating Station
Temple Bruer with Temple High Grange
Medicine Lodge, Kansas
Pipersville, Wisconsin
Ridgway State Park
Pixley, Kansas

New Somerset is an unincorporated community in northern Knox Township, Jefferson County, Ohio, United States.
 It lies along State Route 213 approximately 5 miles (8 km) south of the unincorporated community of Hammondsville and 15 miles (24 km) north of the city of Steubenville, the county seat of Jefferson County.
 It lies somewhat more than 1 mile (nearly 2 km) southeast of the Yellow Creek, a small tributary of the Ohio River, which itself is located 4 miles (6½ km) to the east of New Somerset.
Goshen is a city in and the county seat of Elkhart County, Indiana, United States.
 It is the smaller of the two principal cities of the Elkhart-Goshen Metropolitan Statistical Area, which in turn is part of the South Bend-Elkhart-Mishawaka Combined Statistical Area.
 It is located in the northern part of Indiana near the Michigan border, in a region known as Michiana.
 Goshen is located 10 miles southeast of Elkhart, 25 miles southeast of South Bend, 120 miles east of Chicago, and 150 miles north of Indianapolis.
 The population was 31,719 at the 2010 census.
 The city is known as a center of manufacturing for recreational vehicles and accessories, the home of Goshen College, a small Mennonite liberal arts college, and home to the Elkhart County 4-H Fair, one of the largest county fairs in the United States.
Barber County (county code BA) is a county located in the south-central portion of the U.S. state of Kansas.
 As of the 2010 census, the county population was 4,861.
 Its county seat and most populous city is Medicine Lodge.
 It was named for Thomas Barber, an abolitionist who was killed in Douglas County in 1855 during the Wakarusa War.
Wirock is an unincorporated community between Bondin and Iona Townships in Murray County, Minnesota.
 It is located 5 miles west-northwest of the town of Fulda and about 4 miles southeast of the town of Iona.
The Gibson Generating Station is a coal-burning power plant located at the northernmost end of Montgomery Township, Gibson County, Indiana, United States.
 It is close to the Wabash River, 1.5 miles southeast of Mount Carmel, Illinois, 2 miles south of the mouth of the Patoka River, and 4 miles south of the mouth of the White River.
 The closest Indiana communities are Owensville 7.5 miles to the southeast of the plant, and Princeton, 10.5 miles to the east.
 With a 2013 aggregate output capacity among its five units of 3,345 megawatts, it is the largest power plant run by Duke Energy, the third-largest coal power plant in the world, and the tenth-largest electrical plant in the United States, With the reduction of Nanticoke Generating Station, it became the largest coal power plant in North America by generated power late in 2012.
 Also on the grounds of the facility is a 3000 acre large man-made lake called Gibson Lake which is used as a cooling pond for the plant.
 Neighboring the plant is a Duke-owned, publicly accessible access point to the Wabash River near a small island that acts as a wildlife preserve.
 This is the nearest boat-ramp to Mount Carmel on the Indiana side of the river.
 Located immediately south of Gibson Lake, the plant's cooling pond, is the Cane Ridge National Wildlife Refuge, the newest unit of the Patoka River National Wildlife Refuge and Management Area.
 Opened in August 2006, this 26 acre area serves as a nesting ground for the least tern, a rare bird.
 Cane Ridge NWR is reportedly the easternmost nesting ground for the bird in the U.S.
 The Gibson Generating Station is connected to the power grid via five 345 kV and one 138 kV transmission lines to 79 Indiana counties including the Indianapolis area and a sixth 345 kV line running from GGS to Evansville and Henderson, owned by Vectren and Kenergy.
Temple Bruer with Temple High Grange was an extra-parochial area area in Kesteven, Lincoln, which had in the Medieval period been held by the Knights Templar and later by the Knights Hospitaller of Temple Bruer Preceptory.
 By an Act Parliament passed on the 5th March 1879, Temple Bruer with Temple High Grange was constituted as a parish.
 At that time the parish was in Flaxwell wapentake, Sleaford Union and County Court district, and the ecclesiastical rural deanery of Longobody.
 The parish lies 10 miles to the southeast of Lincoln, 4 miles southeast of Navenby and 6 miles northwest of Sleaford.
 Wellingore and Welbourn parishes lie to the west and Brauncewell to the south.
 The old Roman Road, Ermine Street, passes through the western edge of the parish, which at this point is a bridleway not a modern road.
 Temple High Grange is part of the parish.
 The parish covered about 3,900 acres.
 The parish is now within the electoral area of Ashby de la Launde and Cranwell Ward in North Kesteven District Council
Medicine Lodge is the most populous city in and the county seat of Barber County, Kansas, United States.
 As of the 2010 census, the city population was 2,009.
Pipersville is an unincorporated community in the town of Ixonia in Jefferson County, Wisconsin, United States.
 It is located at the intersection of Jefferson County Roads P and E, about 4 miles southeast of Watertown.
Ridgway State Park is a state park located in Ouray County, Colorado.
 It is the westernmost state park in Colorado.
 The park is 21 miles southeast of Montrose, 14 miles northeast of Ouray, it is also 4 miles north of the town of Ridgway and 312 miles southwest of Denver.
 The current wildlife consists of deer, coyotes, rabbits, and elk.
 Due to the park's variety of animal life, the park is used as a hunting ground although hunting opportunities are extremely limited due to proximity to developed areas.
Pixley is an unincorporated community in Barber County, Kansas, United States.
 Pixley is 4 mi southeast of Medicine Lodge.