I think a call here is probably getting just about right pot odds. Based on the play here I would limit his range down to about AA, AK, KK, or KQ. If you think he is crazy enough to raise UTG with 88 or KJ you should add those to his range as well. Here are the combinations 6 AA, 8 AK, 1 KK, 6 KQ.
Against AA you have 9 diamond outs, 2 K outs and 3 Q outs.
Against AK you have 12 outs
Against KK you have 8 outs
Against KQ you are freerolling for 9 outs
If he has the A
in his hand you have one less out. In the end you are averaging about 13 outs, so 30%ish which is just about the same as the 3:1 pot odds you are getting on a call.