The scrollbar issue seems to be that it puts the scrollbar into the code box rather than outside of it. I don't know if you can get the scrollbar outside of the code box, but if not, then I think your only real option is to automatically insert 1-2 <br>'s or <p>'s after all code in a code tag. That will give you the necessary height you need.
I don't think just putting a minimum height for the code box will work because the vertical scrollbar may not appear if you have just the right numer of lines for the height of the code box, which will result in the bottom line being hidden by the horizontal scrollbar. I could be wrong about that, though. I don't have UBB to test with.
