The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  4 12  1  1  1  8  2  0  2  2  1  2  2  4  1
 0  2  0  2  0  0  6 14  4  4 10  6 12  6 10  2 14 10  4 12  2  0 14 10  2  2  2  4  8  6  2  0  2  0
 0  0  2  2 12  6  6  4  4  2  6  0  8 10  4  2  4  2  2  2  0  6 14  0  4 10  6 14  6 10  4 10  2  0
 0  0  0  8  0  0  8  0  0  0  8  8  8  0  8  0  8  0  8  8  0  8  0  0  8  8  8  0  8  8  8  8  8  0
 0  0  0  0  8  0  8  0  8  8  0  0  0  8  0  8  0  0  8  8  0  8  0  8  8  0  8  0  8  8  8  0  8  0
 0  0  0  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  0  8  8  0  8  0  0  8  8  8  8  0  8  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+51x^28+160x^29+464x^30+552x^31+967x^32+1250x^33+1406x^34+1132x^35+1014x^36+614x^37+342x^38+104x^39+72x^40+22x^41+26x^42+4x^43+7x^44+2x^45+2x^46

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 0.523 seconds.