I think a good starting point may be this:

[![enter image description here][1]][1]

I used `Limited Dissolve` mode from <kbd>X</kbd> 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 (<kbd>Ctrl</kbd>+<kbd>N</kbd>) and made them point outside.

[![enter image description here][2]][2]



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).

[<h3>blend file here</h3>][3]


  [1]: https://i.sstatic.net/DLkbi.jpg
  [2]: https://i.sstatic.net/jatVn.jpg
  [3]: http://blend-exchange.giantcowfilms.com/b/396/