The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  2  1  2  2  1  1  1  2  1  1
 0  8  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  8  0  0  0
 0  0  8  0  0  0  0  0  0  0  0  0  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  0  8  0  0  8  8  0
 0  0  0  8  0  0  0  0  0  0  0  0  8  8  8  8  8  0  8  8  8  8  8  0  0  8  0  0  0  8  0  8  0  0
 0  0  0  0  8  0  0  0  0  0  0  8  0  8  8  0  8  8  8  0  8  0  8  0  8  8  0  0  8  0  8  8  0  0
 0  0  0  0  0  8  0  0  0  0  0  8  0  0  8  8  8  8  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  0  0  8  8  0  0  8  0  0  0  8  8  8  8  8  8  0  0  8  0  0  0
 0  0  0  0  0  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  0  0  8  8  0  8  8  8  8  8  0  0  0  0
 0  0  0  0  0  0  0  0  8  0  8  8  8  8  0  0  0  0  8  0  0  8  8  0  8  0  0  8  8  0  8  0  0  0
 0  0  0  0  0  0  0  0  0  8  8  8  8  0  0  8  8  8  8  8  0  0  8  8  8  0  0  8  8  8  0  8  0  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+80x^24+49x^26+115x^28+32x^29+77x^30+160x^31+130x^32+320x^33+6271x^34+320x^35+110x^36+160x^37+130x^38+32x^39+58x^40+92x^42+15x^44+33x^46+3x^48+3x^50+1x^58

The gray image is a code over GF(2) with n=272, k=13 and d=96.
This code was found by Heurico 1.16 in 0.772 seconds.