The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  0  1  1  1  1  1  1  1  1  1  2 12  1  2  1  1
 0  2 12  6  0  6 12 10  0  6 12 10  4 10  6  6  0  0  2 14 12 12 10 10 10  8  0  4 10  2  2  6  6 10
 0  0  8  0  0  0  0  8  0  8  0  8  8  0  8  0  0  8  0  8  8  0  0  8  8  8  8  0  0  8  8  0  8  8
 0  0  0  8  0  0  0  8  0  0  8  8  8  0  0  8  8  8  8  0  0  8  8  8  0  0  0  8  0  8  0  0  8  8
 0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  0  0  8  8  0  8  8  0  0  8  8  0  8  8  8  0  0
 0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  0  8  0  0  8  0  0  8  8  0  0  8  0  8  8  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+30x^29+48x^30+142x^31+155x^32+532x^33+250x^34+532x^35+128x^36+142x^37+48x^38+30x^39+4x^40+5x^42+1x^58

The gray image is a code over GF(2) with n=272, k=11 and d=116.
This code was found by Heurico 1.16 in 0.0586 seconds.