The most common cause of this is a bad wall control or the wiring going to it. Remove the wall control and disconnect the wiring to the back to eliminate the wall control. You can eliminate both possibilities by disconnecting the wire going to terminal #1 on the back of the motor unit.

The DIP switches for changing the code should be on the rear of the motor unit, beside the up/down force adjustments.
It can also be that something else in your area is using the same radio frequency that your remote control does and is triggering your door. Most GDOs work on a government-preserved frequency, making them susceptable to interference, though your transmitter isn't powerful enough to interfere with their equipment.

If you have an old dip switch unit it might be time to upgrade to a rolling code unit.

There are only 256 combinations on the octal dip switch units, and they can be scanned through in just a few seconds to open the door.

The rolling code is the same thing used on cars now, and is very secure.