The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+154x^16+160x^17+522x^18+528x^19+1059x^20+1376x^21+2031x^22+2432x^23+2788x^24+3672x^25+3186x^26+3604x^27+2960x^28+2640x^29+1956x^30+1372x^31+1087x^32+440x^33+468x^34+124x^35+141x^36+32x^37+29x^38+4x^39+2x^40

The gray image is a code over GF(2) with n=52, k=15 and d=16.
This code was found by Heurico 1.16 in 29 seconds.