Once the Heroic Race is finished it might take a few hours for the claim button to appear in your game.
As soon as it does appear, you can claim your reward directly from the Heroic Race island or from the floating icon at the right side of the screen.

But remember that to be ELIGIBLE to earn ANY REWARDS, you must have at least REACHED LAP 5.

If you have made it to this lap, it means that were QUALIFIED for the rewards and depending on what position was at the end of the race (1st - 8th position) you will be able to claim well-fought winnings!