Adminimize does not work with Contact Form CFDB7

Probably it’s not Adminimize that is to blame, it’s CFDB7 that is not available for any other user but of type Administrator, it’s defined by WordPress access rights – thing working at a deeper level than Adminimize that is just hiding the menus you don’t want to show.

So you may try user role editor plugin (free), you’ll find the capability cfdb7_access there, turn it on for the needed user type (others than Administrator) – it should become visible.