I live in an apartment complex and am using a wire to the red antenna
jack, I think. I thought about connecting it to my rain gutter
somehow.

Hehe, just make sure you remove that antenna from the radio when lightning
approaches!
I only mentioned the larger antenna system/phasing as a personal comparison in
my listening experience, please don't think it was a suggestion for you to go
to the trouble to do the same. The DSP function becomes more attractive when
you are using less of an antenna and have more home/apartment/building 'noise'
than other folks. In your case, you should see more help from the DSP's noise
reduction (if used conservatively) than I do, given our differing antenna
set-ups.
Just take a length of wire, attach a little, metal alligator clip to the
outside end, and clip it to your rain gutter wherever it is the closest or most
convenient. The other end of the wire goes into your red clip input on the
radio. Undo that clip connection if there's any lightning, and throw the lead
outside the window (making sure it's retrievable later, of course).
Linus