The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+67x^28+318x^29+535x^30+1166x^31+1874x^32+2910x^33+2806x^34+2796x^35+1791x^36+1258x^37+498x^38+192x^39+69x^40+58x^41+30x^42+4x^43+6x^44+3x^46+2x^47

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 1.61 seconds.