I think a good starting point may be this:
I used Limited Dissolve
mode from X menu. It effectively gets rid of mess edges and faces of the mesh.
Then I used some very basic tweaking like dissolving some edges and vertices to make them not repeat each other, and creating some new edges instead of old ones. I also recalculated normals (Ctrl+N) and made them point outside.
Finally, I added Shrinkwrap modifier, imported original mesh again and wrapped my result atop of it so to be sure (hope so) that the form of the original mesh was preserved (the original mesh is hidden on the screenshot).