Which four element subsets of {0, 1, 2, ..., 15} have the feature, that their elements sum up to 30?

There are 86 sets with this feature. They are all listed in this file.

Each of the 13 colored squares shows 4 of them. So the colored squares show 13*4=52 sets.
Example: The green fields in the uppermost colored square: {1, 7, 8, 14} ^{(zoom in)}
1 + 7 + 8 + 14 = 30

The 34 black squares below show 34 sets.
Example: The uppermost black square: {3, 5, 7, 15}
3 + 5 + 7 + 15 = 30