Not too far, in that time. It's kind of hard for other people to plan a route, since we don't know what your particular interests are, but here's one plan that could work:
From Casa, take an overnight train to Tangier, then the boat to Algeciras. Stop in Seville or Cordoba en route to Madrid, then from Madrid to Barcelona, up the coast to Arles, to Pisa and to Rome.
With the exception of the routes in Spain, the trains are pretty direct, and you may be able to take some night trains to make the most of the time you have in each city.
I like to throw a couple of smaller towns into my itineraries, to have a bit of a change from the cities.
There are seven stops on this route (no need to spend a night in either Tangier or Algeciras), so you could easily take two to three days in each (two maybe for Arles, Seville/Cordoba or Pisa) and have nearly 10 extra to play with, adding on in some cities, for traveling, or for day trips around (Segovia or Toledo from Madrid, Florence from Pisa, Assissi from Rome, for example).
Good luck with your planning, it sounds like an awesome adventure.