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If the gage works out (my guess for 20A would be 8 or 10 ga) I'd say split the light circuit off and make it 220, rewire the lights at the garage end and splice them into the outlet circuit (making 20A circuit to cover lights and outlets), then you'll have one wire running 220 and one running 110. Get a 220 breaker and pop it into your panel, then connect to it (hot, hot, neutral, & ground)

This from a mechanical engineer...so proceed with caution.