A very good case can be made that this is the shroud of Jaques DeMolay. He was the last Grand Knight of the Knights Templar. When King Phillip of France ordered the Order dismantled (he was heavily in debt to them) in AD 1312, DeMolay was tortured before execution. One of his tortures was to be crucified against a heavy wooden door. The guards amused themselves by repeatedly opening and then slamming the door shut. Oh yes, a crown of thorns was also part of that. Following the torture he was laid out on a shroud overnight but recovered to be burned at the stake in 1314. C-14 testing on the shroud gave a date in the range 1260 to 1390