Here's my first attempt at a barge design un SketchUp.
First attempt indeed ... Design is very crude to allow easy build from plywood (and more honestly because my 3D modeling skills are seriously lacking).
General design comes from barge pictures found on the internet, mostly on Model Tug Forum.
I have absolutely no idea whether those skeggs would prevent barge from drifting or spinning. They're supposed to act as "rails".
Obviously there's still some modeling work required for the inside of the hull: stanchions, beams, maybe even compartments.
I also have to get the measurments of 2-litre soda bottles to make sure I could fit four or even six of them to ballast down the barge. Fill'em up at the pond instead of "static" lead ballast.
Deck could be a simple plywood sheet (with beams). Could probably have multiple "modular" deck sheets to switch barge from one application to another ...