This question intrigued me so much, I wrote myself a little program to work out what the best 4 types are!! The answer I came up with is the same you have - 14 types. You can't get any more coverage than that. There are 3 combinations:
- Ice, Fighting, Ground, Flying - covers everything except Water, Psychic and Ghost.
- Ice, Fighting, Ground, Ghost - covers everything except Water, Fighting and Bug.
- Ice, Fighting, Ground, Dark - covers everything except Water, Fighting and Bug.
So if you want move combinations, clearly the types Ice, Fighting, Ground are the best way to go. They appeared in most of the high numbers (e.g. Ice, Fighting, Ground, Psychic is SE against 13 types).
As for actual Pokemon that can learn good moves of those types... well that's another challenge. There are a few as already mentioned: Gliscor, Beartic, Weavile, Gallade, Electivire. I'm sure there are many.