The MusicMan hardshell case will fit the AX40. It has a notch in the top that allows you to keep the trem bar attached.
I also like the Gator Lightweight Electric Guitar Case. It's a polyfoam case, so it's much lighter than a hardshell case. But it does a great job of protecting the guitar. I have one for my Reflex. I can't comment on keeping the trem bar attached in the case. The Reflex trem bar is easier to remove, and I detach it when I put the guitar in the case.