The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  2  1  2  1  4  1  4  2  1  1  2  1  2  2  4  1  1
 0 12  0  0  0  4 12  4  0  8  0 12  4 12  4  0  8  8 12  8 12  4 12  0 12 12  8  0  8 12 12  0
 0  0 12  0  4  4 12  0  0  0  4 12  4  4  4  4  4  0  8  4 12  0  4  8  0  8  4  4  8  0  0  0
 0  0  0 12  4  0 12  4  0  4 12  4  0  4  8 12  0  4  4  8 12  4  4  4  0  8 12 12 12  0  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  8  8  0  8  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  0
 0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  0  8  8  8  8  8  8  0  0  0  8  8  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  0  0  0  8  8  0  8  8  0  8  8  8  8  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  8  8  8  0  8  8  0  8  8  0  8  0  0  0  8  0  0  8  8  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+51x^22+50x^23+196x^24+228x^25+397x^26+452x^27+855x^28+1428x^29+3139x^30+5996x^31+7097x^32+6040x^33+3142x^34+1504x^35+906x^36+456x^37+381x^38+178x^39+136x^40+36x^41+53x^42+12x^43+23x^44+4x^45+5x^46+2x^48

The gray image is a code over GF(2) with n=256, k=15 and d=88.
This code was found by Heurico 1.16 in 8.72 seconds.