"Muchísima gracias" or "Muchísimas gracias"
I think it pluralises as per the norm and therefore the latter.
You hear the former a lot in lazy speech mind...
Alex and Sabor are both right.
Additionally, there is no such thing as "more correct." Something is either correct or incorrect.
"Muchísimas gracias" is textbook correct. It is plural, there for muchísimas is technically proper. This is a bit of a "textbook phrase" though. It's not often that someone wastes the time to say it.