The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+250x^28+1576x^29+4134x^30+8766x^31+15373x^32+22130x^33+26190x^34+22624x^35+15774x^36+8740x^37+3600x^38+1334x^39+458x^40+98x^41+6x^42+12x^43+6x^46

The gray image is a code over GF(2) with n=272, k=17 and d=112.
This code was found by Heurico 1.16 in 67.8 seconds.