You might want to specify the language you're searching for a project in. About a year ago I wrote a client and server for four-dimensional go in C++ with Qt. It is about 4,000 lines of code if I remember correctly, and should work on both Windows and Linux.
The code abuses exceptions, tight coupling (I think there's even bad friendship somewhere in there), RTTI, uses a ridiculously bad network protocol (which is entirely undocumented), and has at least two classes that do way too much (
Client). Oh, and it lacks any kind of unit tests. It took me about three weeks to write if I remember correctly, so it may be too small.
Feel free to contact me with questions/complaints if you choose to use it.
I think an interesting way of generating such projects would be to take existing student projects and then demand that students add features to them in a timespan that is not quite long enough. After a few of those, which probably get tacked on quickly, you could teach them to refactor and then request another feature at the end (in a similar time slot) to further demonstrate the benefits of what they've learnt/done.