Four years later, Heinz qualified for her second Luxembourgian team, as a 23-year-old, at the 2004 Summer Olympics in Athens. She attained B-standard entry times of 26.41 (50 m freestyle) and 57.14 (100 m freestyle) from the European Long Course Meet in Luxembourg. In the 100 m freestyle, Heinz edged out Hungary's Ágnes Mutina to take the fifth spot in heat three and thirty-sixth overall by 0.70 of a second, with a time of 57.40. In the 50 m freestyle, Heinz touched out Iceland's Ragnheiður Ragnarsdóttir to a fifth-heat triumph by a single hundredth margin (0.01), breaking a Luxembourgian record of 26.35 seconds. Her storming victory was not insufficiently enough to put her through the semifinals, as Heinz placed thirtieth out of 75 swimmers in the morning preliminaries.