The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  2  2  1  1  2  1  1  1
 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  0  0  2  0  0  2  0  2  2  0  2  2  2  2  2  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  2  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  0  2  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  0  2  2  0  0  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  2  2  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  2  2  0  2  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+74x^16+39x^18+92x^20+32x^21+54x^22+160x^23+176x^24+320x^25+177x^26+320x^27+96x^28+160x^29+124x^30+32x^31+69x^32+97x^34+4x^36+14x^38+7x^42

The gray image is a code over GF(2) with n=52, k=11 and d=16.
This code was found by Heurico 1.16 in 0.159 seconds.