How can I amplify my transmitter's RF signal to open the garage from the 12th floor?
If you are interested in a project then boosting your transmitter may be a good route.

If you are interested only in solving the problem in the simplest way, I would recommend you consider a different route. Can you get internet access in the garage? Using either the building's network or a wireless access point or perhaps your vehicle? If you can you can use a wifi based solution like this to open the garage door from anywhere in the world.

I am still unclear why a person would want to do that seeing as I am usually interested in the door only while I'm in there. Would you mind elaborating on your use case?