Even with the bounty in play, I think, you have to many people left to act after you to get involved with a hand as bad as 66, and you also have to many chips. The issue is, that even though you are only risking 7BB against UTG, other people are going to want his bounty as well, and you have up to 38BB at risk against them. If you had like 10-14BB, and it was a very juicy bounty, then maybe there is a case for overjamming and make this the spot, where you make a stand and try to chip up. But with your stack size I would snap fold. Preserving that stack is more important than winning a bounty here and now.
I also dont think your min-raise does anything other than lose you more chips, when the chip leader decides to jam on you. Its not going to deter the shorter stacks from entering the pot, since putting in 7BB would commit them anyway. So if I was forced to get involved here, I would just call and then make a decision based on, who jams on me. Against the chip leader almost certainly folding, against the shorter stacks almost certainly calling.
As played you put in a third of your stack, and the chip leader could certainly be jamming light, so I think, you have to call it off. Its not a great spot, but you are getting 2:1 against him, and you will be flipping more often than dominated. You could even from time to time be ahead of a hand like a suited wheel ace or a smaller pair.
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