Either the owners manual or the service manual warns that the Homelink (the remote in the car) won't accept certain kinds of garage door codes. I don't recall what kind.
I think there was a lower line ceiling console trim for the Gen 8 Riviera, it consisted of a compartment in which you could place a garage door opener, with button extensions such that when you close the compartment up you could push a button and actuate the remote you had put in the compartment. Get any color and paint it to match your car with interior paint mixed at a paint store and put into a rattle can for you.