Unless I'm reading this wrong, GPIO4 is being used as a radio transmitter, but it can only do between 100.025Mhz and 99.975Mhz frequencies. Garage openers work mostly on 315 and, older ones, on 390 MHz.
I don't think the pi ships with a proper software defined radio.
The GPIOs generate (approximate) square waves with harmonics at 3 times the fundamental frequency, then 5 times, 7 times, etc. You can apparently use a filter to select only the third harmonic and transmit on 315 MHz that way.
I don't think the pi ships with a proper software defined radio.