It's kind of odd to imagine not being able to think of anything to do on a system or codebase. Do you need approval before starting on a change? Why not just do something that makes things better?
Also, they don't want changes made unless there is a need because they don't want to risk new bugs being introduced.
You should understand the system both technically (how is it architected, how does it work, what does it do) and from a business standpoint (why does it do that? where is value derived? what is painful?).
It's hard to add value if you can't be entrepreneurial or innovative.
You said that you complete things as soon as possible. Are you sure that you are understanding the problem? The solution?