Ignoring the turn and river cards (IE as far as I know villain can have a K much easier) (and you should delete everything past your last action):

/me agrees with Fallen Hero. Your kings are obviously no good, so you are at best 1.5 to 1 behind (=fold). If bb has 44 you're behind even more than that.

Edit: ok BB only called a minraise, so your kicker might be ok (edit2: ignoring KQ...), so maybe you can call here. I think it's pretty close. I still like to have some fold equity if I'm playing this particular draw for my stack.