I agree with Camilo and Rob. If you want to make a cladogram, you need to use software that does parsimony analysis. Other methods that are not based on parsimony produce phylogenetic trees, but they are not cladigrams.
Based on your presence/absence matrix (0/1) of known mutation, you can construct a dendrogram using several methods (e.g : Neighbour-Joining ), distances (Jaccard or Euclidean etc) and bootstrapping with PAST software (Past 3.x - the Past of the Future).
Here is the link : http://folk.uio.no/ohammer/past/
I agree with Andrew Brower. So, I prefer to use methods that produce phylogenetics tree. Dear Simone, you can try to describe the characters instead to use only present/absent. Your phylogenetic proposal will be more informative and coerent. I use TNT too, more with (0) for plesiomorphic state, and (1, 2.....) for apomorphici state. Good luck.