The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+81x^28+214x^29+613x^30+1054x^31+1766x^32+3230x^33+2578x^34+3234x^35+1683x^36+1010x^37+570x^38+178x^39+113x^40+26x^41+10x^42+14x^43+4x^44+5x^46

The gray image is a code over GF(2) with n=272, k=14 and d=112.
This code was found by Heurico 1.16 in 1.38 seconds.