How do I change the permission set for a code group?

Use caspol. If you are the machine administrator, you can operate at the 'machine' level - which means not only that the changes you make become the default for the machine, but also that users cannot change the permissions to be more permissive. If you are a normal (non-admin) user you can still modify the permissions, but only to make them more restrictive. For example, to allow intranet code to do what it likes you might do this:
caspol -cg 1.2 FullTrust
Note that because this is more permissive than the default policy (on a standard system), you should only do this at the machine level - doing it at the user level will have no effect.