The generator matrix

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

generates a code of length 32 over Z16 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+34x^20+100x^22+12x^23+158x^24+108x^25+332x^26+432x^27+1343x^28+1264x^29+3659x^30+6376x^31+5090x^32+6376x^33+3677x^34+1264x^35+1400x^36+432x^37+338x^38+108x^39+136x^40+12x^41+70x^42+23x^44+15x^46+7x^48+1x^50

The gray image is a code over GF(2) with n=256, k=15 and d=80.
This code was found by Heurico 1.16 in 7.39 seconds.