The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  4  2  1  0  1  2  4  1  1  4  2  2  1  1  2  1
 0 12  0 12  0 12  0 12  0 12  8 12  4 12  0 12 12 12 12  4 12 12 12 12  0 12 12 12  0  0  0 12
 0  0  8  0  0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  0  0  0  8  0  0  8  8  8  8  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  0  0  8  0  8  0  8  8  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  0  0  8  8  0  8  8  0  8  0  8  8  0  8  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  8  0  0  0  8  8  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  0  0  0  8  8  8  0  8  8  8  8  8  0  8  0  0  0  0  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  8  0  0  8  8  8  8  0  8  0  8  0  0  0  0  8
 0  0  0  0  0  0  0  0  8  0  8  8  0  8  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  8  8  8
 0  0  0  0  0  0  0  0  0  8  0  8  8  8  0  0  8  8  0  8  0  0  8  8  0  0  8  0  0  8  8  0

generates a code of length 32 over Z16 who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+52x^22+18x^23+113x^24+46x^25+151x^26+160x^27+514x^28+848x^29+1358x^30+4052x^31+1810x^32+4060x^33+1275x^34+816x^35+540x^36+160x^37+200x^38+74x^39+75x^40+6x^41+29x^42+18x^44+6x^46+1x^48+1x^50

The gray image is a code over GF(2) with n=256, k=14 and d=88.
This code was found by Heurico 1.16 in 2.56 seconds.