We're staying in Beijing with The 72 Hour Free Visa.

I Will appreciate very much if someone could advise me if we could visit The Great Chinese Wall (one of te closest section a to The capital) with the free transit. I understand that there is a certain geographical restrain and I'm not sure if a day trip to The Wall will not be allowed.
I'd also appreciate if someone could recommend the best way to get to The Wall in a budget.
Thanks in advance!