AK in a 4 bet pot vs 2x shove

no real reads on villain as small sample size. i ended up making one of the tightest folds possible, i know i am unblocking the flush draw but the only hands that make sense to me are JJ, AJ and maybe AK too. Thoughts on this persumably terrible fold?

5NL Zoom

BTN: 98 BB
SB: 183.4 BB
BB: 156.8 BB
Hero (UTG): 197.8 BB
MP: 112.4 BB
CO: 162.6 BB

SB posts SB 0.4 BB, BB posts BB 1 BB

Pre Flop: (pot: 1.4 BB) Hero has Kh Ah
Hero raises to 2.4 BB, fold, CO calls 2.4 BB, fold, fold, BB raises to 12 BB, Hero raises to 25.6 BB, fold, BB calls 13.6 BB

Flop : (54 BB, 2 players) Jc 4d Ac
BB checks, Hero bets 13 BB, BB raises to 131.2 BB and is all-in

Hero ??