hi Mirac78
I install and repair Electric gates now and then,, so i am familiar with the controllers and remotes. The remotes that are used in the electric gate/Shutter industry are mainly a rolling type code (code is always changing), but the remotes and the controller can be configured to work on static codes also, to answer your question there is no easy way to do it, I have a home automation controller that i designed that "may be" up to the task, but it's not "available" yet and I don't know if it ever will be.
I have already pushed this idea to my current customer who wants an electric gate fitting. I'll be going today to inspect the work carried out by the gate manufacturer and tomorrow I may install the electrical side of things.
I could keep you posted if you like.
edit: the remote you have for your shutter is not a rolling code remote. I also think your remote can be emulated with my gadget.