C(13,3,2) <=26

Method of construction: random greedy covering

 9 12 13
 6 11 12
 7  9 11
 3  4 11
 4  5  7
 2  5 12
 5  8 11
 8 10 13
 1  3 12
 7  8 12
 2  3  7
 2 10 11
 2  6  9
 1  7 10
 3  8  9
 1  5  6
 5  9 10
 1 11 13
 4  6  8
 3  6 10
 2  4 13
 1  4  9
 1  2  8
 4 10 12
 6  7 13
 3  5 13