The generator matrix

 1  0  1  1  1  6  1 12  1  1 14  1  2  1  1  1  8  1  1 14  1 10  1  8  1  1 14  8  1  1  8  4  1  2
 0  1 11  6 13  1  8  1 11 13  1  2  1  3  6  4  1  5 15  1  6  1  1  1  2 10  1  1  9  5  0  4 11  0
 0  0 12  0  4  0  0  8  8  0  8  0  0  0  4 12  4  4  4 12  8  4 12  8  4 12  8 12  4  4  4 12  0  4
 0  0  0 12  0  0  4  8 12  4 12  4 12  0  4  8  8 12  4  0  0 12  8 12  8  4  4  0  4 12 12 12 12  4
 0  0  0  0  8  0  8  8  8  0  8  8  0  8  8  8  0  0  8  8  0  0  0  0  8  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  8  0  8  0  0  0  8  8  0  8  8  0  8  0  8  8  0  8  0  0  8  8  0  0  8  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+125x^28+228x^29+596x^30+1176x^31+1800x^32+2908x^33+2693x^34+2992x^35+1791x^36+1212x^37+509x^38+184x^39+107x^40+4x^41+39x^42+16x^44+3x^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 1.63 seconds.