The forty-first academy marathon, over a distance of forty kilometers, was held in April of 2323 on the planet Danula II. Jean-Luc Picard passed four upper classmen on the last hill, becoming the first, and as of 2367 the only, freshman cadet to win the marathon. A considerable amount of training preceded it. (TNG: "The Best of Both Worlds, Part II", "Chain of Command, Part I"; Star Trek Nemesis)
Admiral J.P. Hanson described this as "the damndest thing I ever saw", and decided to make getting to know Picard his business, a sentiment he recalled after Picard was converted into Locutus of Borg in 2366. Picard kept a certificate pertaining to the win in the Picard family album. (Star Trek Nemesis)
Along with the rest of the family album, this certificate was initially created for Star Trek Generations, though it was not seen in the film. Certificate artwork was included in a behind-the-scenes feature of Star Trek: The Magazine Volume 3, Issue 3, p. 70 in July 2002 (missing the last line of text.) A clear shot of the prop certificate used in the album was shown as part of a special Star Trek episode of Let's Make a Deal in February 2019.
The distance, forty kilometers, is slightly shorter than the modern marathon by approximately two kilometers, or just over one mile.
According to his dossier on the official Star Trek site, in the alternate reality Pavel Chekov won the Academy marathon some time before his mission on the USS Enterprise in 2258, and was the youngest cadet to do so at the time.  In The Gemini Agent, Chekov was depicted training for the event by running barefoot, and indicated the previous record holder was 18 years old at the time.