You can NEVER fold this flop. The pot is 240 and you have 426 behind. Check folding is bad. Bet folding is an absolute horror show.
I took the time to run some calcs in pokerstove. Assuming villain never has AJ, JJ, TT or 44, as its much more likely that he will just 3bet shoves those hands pre, I gave villain this as a "not folding the flop" range.
Thats every combo of hand that fits in what a speculative flat call that connects with this flop. So assuming we bet these are the hands that villain continues with. Vs that range with AcKc here we have 47.8% equity on this flop, so given that the pot is well over 50% of our stack I would bet call here all the time. There are plenty of hands villain can fold and we are in pretty decent shape when he doesnt fold. Even if you bet 120 on the flop, villain reshoves, turns over his cards and shows you QJ offsuit, you still have to call