The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  2  0  1  1  2  8  1  1  0  1  0  1  1  1  1  2  2  1  1  1  8  2
 0  2  0  6  0 14 10  8  6  8  2  8  6  2  2  6 14  2  8 12  2 10  2  4  2  6  0 14  0  4  2 12  2  0
 0  0 12  0  0  0  0  4  4  8  4  4  0  4  4  4  8  4 12  8  4 12  8  0  8  0 12  4  0 12  8  0 12  8
 0  0  0 12  0  8 12  0 12  4 12 12  0  8  8  0  4  0 12  4  4  4  0  4  8  8  4  4  4 12  0  0  8  8
 0  0  0  0 12 12  4 12  8  0 12  4  8 12  0 12  0  8  8 12  0  0  8  0 12  8  4  4  4  0 12  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+136x^28+44x^29+380x^30+348x^31+1070x^32+1148x^33+2030x^34+1128x^35+998x^36+372x^37+338x^38+28x^39+112x^40+4x^41+34x^42+18x^44+2x^46+1x^48

The gray image is a code over GF(2) with n=272, k=13 and d=112.
This code was found by Heurico 1.16 in 0.696 seconds.