What a great journey of discovery!
I’m assuming your great grandfather was full Native, as well as your grandmother (meaning both their parents were full Native). If this is the case, this would make one of your parent’s half Native (depending on whether your grandfather was Native or not). This would make you one-quarter Native.
If you’re looking to find out more, see if you can get more information from your family. Asking around is great way to discover more about your lineage. If you discover more, contact your tribal office and talk with the enrollment department. You can do a simple internet search for their information.
Best of luck on your journey!