The generator matrix

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

generates a code of length 34 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+38x^28+84x^29+106x^30+354x^31+354x^32+604x^33+1075x^34+592x^35+341x^36+318x^37+82x^38+74x^39+29x^40+16x^41+13x^42+4x^43+5x^44+2x^45+3x^46+1x^54

The gray image is a code over GF(2) with n=272, k=12 and d=112.
This code was found by Heurico 1.16 in 0.179 seconds.