The generator matrix

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

generates a code of length 26 over Z4 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+45x^14+161x^16+104x^17+372x^18+464x^19+932x^20+1256x^21+1927x^22+2624x^23+2953x^24+3792x^25+3514x^26+3680x^27+3082x^28+2576x^29+1915x^30+1344x^31+934x^32+456x^33+368x^34+80x^35+112x^36+8x^37+49x^38+15x^40+2x^42+2x^44

The gray image is a code over GF(2) with n=52, k=15 and d=14.
This code was found by Heurico 1.16 in 14.6 seconds.