C(12,3,2) <=24

Method of construction: random greedy covering

 2  7 12
 4  5  9
 3  8 12
 4 10 11
 1  2  5
 2  3 11
 7  9 11
 6  7  8
 5  6 12
 1  6 11
 3  4  6
 1  9 12
 5  8 11
 1  8 10
 2  6  9
 1  4  7
 3  5 10
 2  4  8
 7 10 12
 1  3  9
 2  6 10
 8  9 10
 4 11 12
 3  5  7