I had the same problem, since the .ut2mod extension is for UT2k3
Anyway, you have two choices, "open with" and change the extension (last not recommended)
To operate the .ut2mod file, simply hold your LEFT shift key and RIGHT click on the file.
Select "OPEN WITH".
if you are given options, select "CHOOSE PROGRAM"
You should see a list with several programs in it... Look for UT2004
If you can't find it, select "BROWSE"
Look for your UT2004 folder, open it and open your SYSTEM folder.
Select your SETUP.EXE file, located inside your SYSTEM folder.
If done correctly, your .ut2mod files will now look like a paper sheet with a computer on it.
Double-click to run it.
The second, and least recommended option is to simply change the extension of the file to .ut4mod
However, this may corrupt the file, crash the computer or make a bad installation