There is no such combination.
All possible combinations of Pokémon types have at least one type that they're not resistant to. I whipped up a program to test every possible combination, and the closest you can get are apparently the following:
Normal/Fire/Water/Electric/Fighting/Ground/Flying/Psychic/Steel/Fairy, Fire/Water/Electric/Fighting/Poison/Ground/Flying/Dark/Steel/Fairy, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Ghost/Dark/Steel, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Psychic/Dark/Steel/Fairy, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Ghost/Dark/Steel/Fairy, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Psychic/Ghost/Dark/Steel/Fairy
Resistant/immune to everything except Water, which they would be weak to (2x).
Normal/Fire/Water/Fighting/Poison/Ground/Flying/Rock/Ghost/Dark/Steel, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Rock/Ghost/Dark/Steel, Normal/Fire/Water/Fighting/Poison/Ground/Flying/Rock/Ghost/Dark/Steel/Fairy, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Rock/Ghost/Dark/Steel/Fairy, Normal/Fire/Water/Fighting/Poison/Ground/Flying/Psychic/Rock/Ghost/Dark/Steel/Fairy, Normal/Fire/Water/Electric/Fighting/Poison/Ground/Flying/Psychic/Rock/Ghost/Dark/Steel/Fairy
Resistant/immune to everything except Water, which they would be weak to (4x).
Normal/Fire/Water/Electric/Grass/Ice/Poison/Flying/Rock/Ghost/Dragon/Dark/Steel/Fairy
Resistant/immune to everything except Rock, which it would be weak to (4x).