In my area, there is one number to call and they will come out and mark any existing underground electrical wires, telephone and TV cabling, gas lines, water mains, and sewage lines. So that will tell you where you can or cannot dig. So that's one helpful thing to check on.
As for how far away the grounding rod needs to be from anything else down there, I certainly would be hesitant to put my grounding rod too close to a gas line. Logically in my head, any lightning strike that could potentially travel down my home wiring and out to the grounding rod, where it might spread and reach the gas line, would worry me as a homeowner. My worries might be unfounded, but they are still something I'd be thinking about.
I'm sure if you contact the city or the gas company, one or both would have regulations for you on that. The city may have it in their municipal building code. The gas company in their safety and installation guidelines.