For whatever reason, yesterday, I could not open your JPEG file but today it opened up and looking at your crane it is not mobile unless it hase wheels or tracks. Looking at the bed frame of the crane in your picture, a though occured to me that you may want to bolt the crane base on a different bed frame for a 360d of rotation. This bed frame would spread the load on the deck, assumingly, of a barge that is designed to handle a listing and tilting not exceeding OSHA's regulation on cranes mounted on barges.
For a starting point check out ASME.ANSI B30.8 Floating Cranes and Derricks. There is a general statement about the structural support of barges.
In my past employment in bridge construction, we used a lot of barge mounted cranes, but our cranes were either on wheels or tracts and we used mats or dunnage on which we positioned our cranes. Whenever we bought a second barge, we always got background info on the barge from the seller and occasionaly reinforced their internal steel bracing, so the seller may also be able to assist you.
Note, you'll need a revised load chart, on board, for the crane to be used over water.