Genius! Attach it to the roof! Thanks guys
I got a new wheel today and I've cable tied it to the roof bars, I just managed to fit it in! It wouldn't have gone on a wall anywhere and I'm sure it wouldn't have occurred to me to suspend it, so thank you both for the advice.
Domino loves the new wheel, he kept jumping in and spinning it while I was trying to put it up. He can really stretch out when he's running now, he looks great in it