Winning is not required BUT you must finish the race
There are two ways you can do this, either create a custom Endurance race or use the online Hardcore
playlist and hope the Endurance mode comes up. Any time limit counts so if you wish you can get this in a 5minute Endurance (Which does come up in playlists)
The game seems to be quite active online so the public online playlist will be good for this and you could try for this whilst going for Social Butterfly in GRID 2
at the same time.
Here's a video