The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+105x^28+72x^29+400x^30+1128x^31+1993x^32+2896x^33+3260x^34+2896x^35+1950x^36+1128x^37+348x^38+72x^39+92x^40+20x^42+17x^44+4x^46+2x^48

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 1.62 seconds.