The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+97x^30+840x^31+1094x^32+1520x^33+1428x^34+1334x^35+914x^36+636x^37+149x^38+128x^39+23x^40+20x^41+6x^42+2x^43

The gray image is a code over GF(2) with n=272, k=13 and d=120.
This code was found by Heurico 1.16 in 0.3 seconds.