Pushing against big stack

[Isura]

Middle/late stages of $5 + $0.50 pokerroom MTT. Blinds are 400/800 (no ante). I have T6000 and the big stack at the table has T38,000 (he's about 2nd in chips overall). Big stack raises to T3,100. What is a rough minimum hand I can push here with. The big stack get been raising fairly liberally, and on this occasion he opened the pot in 5th position (no other callers between him and me).
There are 40 people left, 10-20 pay 3x buyin, and final 10 has typical payout distribution.

I pushed with AJ, too loose? I'm thinking on PP's and AK, but I fear being blinded out of the real money.