If this is the situation then I'd worry less about the low amperage and focus on getting to most efficient connection (higher voltage) from your box. Maybe larger gauge wire i.e.:6 versus 8.
Thicker wire will definitely get you a higher voltage, but not a whole lot.
For scale, I upgraded my Roadster's charging situation recently, moving from the dryer plug's 30 amp breaker fed with #10 wire to a 50 amp 14-50 using #4 (oversized for future upgrades; #6 is customary). The run was shortened (better location) from about 55 feet to about 40. At the original 24 amp charging rate, the new circuit nets me something like a volt or so higher as reported by the car. It's hard to tell, because it's less than the normal variation of the line voltage from one day to the next. Of course, now I can charge at 40 amps instead of 24, but the voltage gain was pretty minimal. Even at 40 amps, the voltage holds firm. (Yea!)
I also added a pair of dedicated 20 amp 120 volt plugs. Same 40 foot run, this with #12 wire. I tried charging from it, just to try it, and the car reported only 117 volts that time. Note that the 120v direct charging cable is skinnier (#12) than the UMC (#8), but overall it seems to have lost 3-ish more volts than I would have expected. Had I wired it up for 240 volts on a 20 amp breaker (16 amp rate), that would have been a 6 volt drop, which might barely be noticed (2.5%, or 15 minutes in 10 hours charging).
So, TL;DR bottom line: paying attention to wire size does matter. But don't expect miracles.