I have a G36, and I also researched ways to update the firmware.  Never found an answer, so I presume its not something that can be done (or that Arris wants done) at the user level.  I had numerous persistent issues with this gateway and hoped firmware updates would resolve them.  It has worked properly maybe 50% of the time I’ve owned it, which is 11 months.

 The service provider must distribute firmware updates to cable modem devices. ARRIS develops the software update and makes it available to service providers.  The service providers qualify, test, and distribute the software update to devices on their network.  It has limited control or visibility on distribution by the service providers.