The generator matrix

 1  0  0  1  1  1 10 14  1  1  1  2  2  1  1  1  6  6  1  0  1  1  4  4 12  1  1  1  2  6  1  1
 0  1  0  2  1  7  1  6  1 11  8  1  1 12  4 11  8  1  2 14 15 14  1  1  1 11  3  8  8  1  3  0
 0  0  1  1  5  2  1  1  7  0 15  7 10  2  1 15  1  8  4  1  1  6 11 12 14  4 13 12  1  9 10  0
 0  0  0  4 12  8  4 12  0 12  8  8 12  4  0  0  4  8  0  8 12 12  8  4 12  4  0 12  0 12 12  0

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

Homogenous weight enumerator: w(x)=1x^0+72x^27+555x^28+1244x^29+2096x^30+2586x^31+3341x^32+2732x^33+2015x^34+1002x^35+503x^36+144x^37+62x^38+18x^39+8x^41+3x^42+2x^43

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 1.06 seconds.