It's a soft G (= a J sound), as in stingy, grungy, mangy.
I couldn't be sure MM3 and I both understood the same way: as well as mingy, in British slang we also have a (presumably unrelated?) word, minge, which means a woman's pubic hair. I was pretty confident that MM3 didn't mean that! - but where there are two meanings for a word there can easily be three.