How can I programmatically get a list of all Simulink base and custom datatypes

I am creating a custom GUI with GUIDE and I am looking for a way to get a list of all the data types, including custom ones, on the fly to populate a dropdown list in a table. I am using the Data Dictionary if that is a more direct way to pull the list somehow.

As an example I would like to be able to get the data types in ths list in a custom GUI I am working on.