made the mistake of telling us the outcome which clouds the judgement
so im not going to comment on the hand itself, but the players
UTG raise means strong hand (unless notes tell us otherwise)
you have 12bb so not really essential to play 66 so strongly unless you know UTG can find a fold, which wont happen very often, so you know your going to get called by him regardless of holdings and you will either be racing, or dominated.
as it stands button had AA but it was impossible to know based on actions what he has so he is not even in the equation
the only question you should be asking was, could your opponent fold, or will he call you with worse (that means would he call with 22-55 is that in his utg opening range) if it is then make the shove and if button wakes up with AA then unlucky, better hope for your set lol