In that case, it sounds like your compressor setting might have been turned up too high. And it makes things worse if you don't have a noise gate (I'm not sure if there is one in your multi-effect?)

If you don't have a noise gate, you can't stop those unwanted noises from sounding out when you're not playing. Because the compressor raises the volume of ALL sounds, even buzzing.

But adding distortion is probably the quickest way to increase sustain. And like I said turning up the gain dial helps too.

Glad you figured it out.