Check the switch function of the jack.
With amp off, plug in a blank jack or short cable and check the resistance between tip and sleeve. It should be isolated or at least extremely high(Mohms). If using a cable, check the cable by itself(unplugged)
If it's lower, the switching function mqy be an issue. If it's good, you'll need to dive into the circuit.
But if it only makes noise with the cable plugged in, it's either the jack or ground plane issue. I'd start with checking the diodes and caps before the opamp.