The generator matrix

1 0 0 0 0 0 0 0 1 1 1 1 1 2 0 1 0 0 0 2 2 0 1 2 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 3 2 2 1 1 1 2 3 2 3 0
0 0 1 0 0 0 0 0 0 1 2 3 3 1 3 2 1 2 0 2 3 1 3 0 2 0
0 0 0 1 0 0 0 0 1 0 2 1 3 3 0 2 0 1 1 0 3 0 1 1 3 0
0 0 0 0 1 0 0 0 1 1 3 2 1 3 2 0 3 3 3 3 0 1 2 3 2 0
0 0 0 0 0 1 0 0 1 2 1 2 3 0 3 0 3 2 0 1 1 2 0 2 3 2
0 0 0 0 0 0 1 0 1 3 0 3 0 1 3 3 0 1 2 2 3 2 2 2 2 1
0 0 0 0 0 0 0 1 2 1 3 0 2 2 3 1 1 3 3 3 2 0 2 0 0 1

generates a code of length 26 over Z4 who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+42x^15+171x^16+376x^17+719x^18+1140x^19+1742x^20+2744x^21+3819x^22+5184x^23+6296x^24+6804x^25+7335x^26+7052x^27+6160x^28+5076x^29+3858x^30+2894x^31+1858x^32+1060x^33+625x^34+320x^35+154x^36+68x^37+27x^38+8x^39+2x^40+1x^42

The gray image is a code over GF(2) with n=52, k=16 and d=15.
This code was found by Heurico 1.10 in 44.9 seconds.