I don't really understand the flop minraise. You're going to induce shoves from all sorts of marginal hands as well as draws (all of which are probably better than yours).

If you're going to raise, raise to amount with some fold equity ($12-15), or if you insist on raising small, do it with a much stronger draw (AKh's etc) that will get shoved on by worse draws at least.

Though even with AKh's I like a much bigger raise still, to force them to either fold or shove anyhow.

As played, fold turn, cause you have serious reverse implied odds going on. His bet looks like its suckering you in.