Cody started her Paralympic career representing the United States in wheelchair basketball at the 1984 Summer Paralympics. Cody later moved to athletics in her following Paralympic Games and won four silver medals at the 1988 Summer Paralympics. At her final Paralympic Games, Cody won a gold and a bronze at the 1992 Summer Paralympics while achieving a shared world record in the 4 × 100 m relay. In 2013, she ran for vice president of the International Paralympic Committee. While she was defeated by Andrew Parsons, Cody was selected onto IPC's board of directors that year.