It's a leveled item, and unfortunately the top tier version of it (I think) cannot be improved. Ironically a lower tier version in an improved state will probably be a more powerful weapon.
You know what? I have 2 of them (game bugged). One I got in my 40s and one I got in my 60s - I'm going to check both of them at the Grindstone.

Edit: I just checked them and I didn't get the option, but I seem to remember improving the first one I got and not being impressed with it afterward. They are both equal in damage and value though so maybe the first one was maxed when I got it.
