No.
Then it doesnt exist. As far as we know, or suspect, the Shroud was walled up in the city gate in Edessa during that period, and enclosed in a frame that only exposed the face. It was, at that time, referred to as the Image of Edessa after being taken to King Akbar of Edessa to cure him of an affliction. Perhaps what you are thinking of is the cris-crossed grating look of the framework that had an opening to show the face?
This is a very early image of what is purported to represent the Image of Edessa:
It has most of the classic markers for being derived from the Shroud, plus it has the inexplicable dots on either side, and the lattice work image at top and bottom. There is another image of the Image of Edessa that shows the face in the lattice work.
These would have come from a period closer to what you may be thinking of.
Another name for the Image of Edessa was the Mandylion.
Those images of the Image of Edessa or Mandylion are attributed to the 5th or 6th Century.