I would like to get out of the airport and visit the great wall

I have a 13 hour layover in Beijing and would like to use that time to visit the great wall.

Will the 72 hour transit visa work for me? Says the one is to"facilitate the international visitors’ short stay for sightseeing" but also says " Visitors are not allowed to leave the transit city to other cities during the 72 hours"

The wall is less than 40km from the airport would that count as leaving the transit city to go to another city?