The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+154x^29+623x^30+1106x^31+2023x^32+2830x^33+3035x^34+2776x^35+2103x^36+974x^37+439x^38+182x^39+86x^40+38x^41+5x^42+3x^44+4x^45+2x^46

The gray image is a code over GF(2) with n=272, k=14 and d=116.
This code was found by Heurico 1.16 in 1.42 seconds.