Do you have a basement that you could run the wiring instead of outside?
When I added my 220v, I did like Randy is suggesting. I left my dryer circuit as is, and dropped in a new 30 or 40A (can't remember) breaker to the panel, and then ran a short line of hard conduit through the wall and into my basement. I had something like 75' of wire to get from the panel to my garage, and I can't remember what I gauge I used - but I can check. I want to say it was 8g and it was pretty $$.
1976 FJ40 - green and mostly stock
1996 FZJ80 - not so stock