FogBugz supports integrating directly with Google Drive. You can enable it for your team in the Avatar Menu → Integrations → Google Drive.
Once the integration is enabled, you just need to include a reference to any case number in the format of “case XYZ” in the title of any Google Drive document:
This will cause an edit from Google Drive to appear in the case history with a link to that document:
For more information about this topic, read the article Using Integrations in FogBugz.