The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+52x^30+232x^31+243x^32+366x^33+324x^34+356x^35+217x^36+144x^37+38x^38+52x^39+18x^40+2x^41+1x^42+1x^44+1x^50

The gray image is a code over GF(2) with n=272, k=11 and d=120.
This code was found by Heurico 1.16 in 0.0533 seconds.