I don't think it is exactly like that, but with a different move order that is basically a KIA(Kings Indian Attack). You should look up the KIA in the Book Openings section.
Does This opening exist?

4.g3 makes this the Glek system of the Four Knights Game. Look for games where Glek played this as White for a guide.
I was wondering if this opening exists already because I loved the results I got with white!