The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  2  1  4  1  1  1  1  2  1  4  1  1
 0 12  0  0  0  4 12  4  8 12  8  0  0  4  4  4  4 12  4 12  0  0  8  4  8  4 12  0  4  0  8 12  8  4
 0  0 12  0  4  4  4  8  0  4  8  4 12  4  8  0  0  0 12 12  0  4  4  8  8  4 12  0 12  8  4  8  0  8
 0  0  0 12  4  0  4  4  8  0 12  4  8  4  0  4  4  4  0 12  4  8  0  0 12  8 12  4  8  4  8  0 12 12
 0  0  0  0  8  0  0  8  8  8  0  0  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  8  0  0  8  0  0  8
 0  0  0  0  0  8  0  0  0  0  8  0  8  8  8  0  8  8  8  8  0  8  0  0  0  8  0  8  0  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+87x^28+4x^29+202x^30+68x^31+436x^32+696x^33+1164x^34+696x^35+423x^36+68x^37+106x^38+4x^39+98x^40+32x^42+10x^44+1x^56

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 0.214 seconds.