The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+107x^28+4x^29+220x^30+100x^31+493x^32+664x^33+984x^34+664x^35+457x^36+100x^37+156x^38+4x^39+82x^40+48x^42+11x^44+1x^52

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 0.212 seconds.