If you plug direct into an amp does it make the same buzz? If you're using an effect like distortion, a hum is natural but can be mitigated with a noise gate, something that pulls your volume down if it's under a certain threshold. Try sptnk/effect/noise gate near the end of your effects chain if there's space.
Guitars can and do make buzzes anywhere from the pickup to the speaker. Sometimes it's grounding issues, sometimes the jack is a little messed up.