The generator matrix

 1  0  0  1  1  1  6  1  2  1 12  1  4  1 10  1  1  6  1  6  1  1  4  1  2  1  1  1  1  6  2  1
 0  1  0  0  1 15  1 12  4 13  1  1  1  6  1  6  3  1  7 14 12 10  1  1 12 10  0  2 14  1  4 10
 0  0  1  1  1  4  1  4  1  8  1  3 14  3  6  9 15  7  4  1  6  0 11 11  1  7 10  0  9 14  6 13
 0  0  0  2  8 10 10 14  6 12  4 10  2  0  0  2  2  8 12 14  6  2  0  4 12  4  8  6  0 12  6  8

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

Homogenous weight enumerator: w(x)=1x^0+282x^27+1144x^28+2076x^29+4065x^30+5592x^31+6480x^32+5620x^33+4172x^34+1986x^35+922x^36+284x^37+97x^38+28x^39+13x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=256, k=15 and d=108.
This code was found by Heurico 1.16 in 4.12 seconds.