The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+298x^29+1075x^30+2530x^31+3764x^32+5594x^33+6083x^34+5816x^35+4065x^36+2280x^37+801x^38+332x^39+71x^40+34x^41+9x^42+8x^43+3x^44+2x^45+2x^47

The gray image is a code over GF(2) with n=272, k=15 and d=116.
This code was found by Heurico 1.16 in 4.53 seconds.