When I first read your question, I had this funny mental image of a guy in a suit clinging on to a stack of papers with source code on and a bunch of devs trying to yank it from him! :D
Now, I am not a manager, but I would say that I would expect my manager to have an idea of the technologies available (so I feel he is making management decisions based on supporting knowledge). But I would not necessarily expect him to still be actively coding in the same way a developer is/should.
That said, my manager still writes code, just not as much.
I think (and this may be the obvious) "should" is a kinda strong term. I think it depends on your work situation, team size, the amount of actual management they need compared to the amount of code required etc.