The generator matrix

 1  0  1  1  1 10  1  1 14  1  1  6 10  1  1  4  2  1  1  1  1  1  6  1  1  1  2  1  1  1  4  1
 0  1  1  0  3  1  8 11  1 10  3  1  1 10 13  1  1  1  2  0  1  4  1  0  9 14  4  5  6 15  1  8
 0  0  2  0 14  8  2 12  2 14  4  6  4 10  0  4  6 10  0  8 14  4  0  2  0  2  6 12 12  6 14 12
 0  0  0  2 14 14 14  8  6  0 10  8  2 10 12 12 12 14 10  6  8 12  8  4  6  4  6 14  4  0  0  0

generates a code of length 32 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+134x^27+458x^28+1184x^29+1850x^30+3022x^31+3197x^32+3142x^33+1657x^34+1034x^35+443x^36+164x^37+60x^38+18x^39+12x^40+6x^41+1x^42+1x^44

The gray image is a code over GF(2) with n=256, k=14 and d=108.
This code was found by Heurico 1.16 in 1.3 seconds.