A lot of the rolling code generators give you a one in 24 million chance of picking the right code on the next key press. You would be better off piggybacking a hackable receiver with the existing one. I reverse engineered a remote PIR detector once for fun. It had a 24 bit transmission, but it was not encrypted. Once you have a receiver that will pick up the 315 MHz or 433 MHz signal, you can output the data to a standard oldsillyscope. You can send the signal continuously, and record the image to graph paper. Similarly, you can adapt some of the IR decoding software for the PIC, and do it that way.
Ron