The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  1  4  1  1  1  1  1  1  1  4  1  1  2  2
 0 12  0 12  0 12  0  0  4  8 12 12 12  0  8  4 12 12 12  0 12 12  8  8  0  4 12  4  8 12  8  4 12 12
 0  0  8  0  0  0  0  0  0  8  0  8  8  0  0  8  0  8  0  8  0  8  8  0  8  8  8  0  8  0  8  0  0  0
 0  0  0  8  0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  0  0  0  0  8  8  0  0  0  8  0  8  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  8  8  8  0  0  8  0  0  8  0  8  8  8  0  8  0  8  8  0  8  8  8  0
 0  0  0  0  0  8  0  0  8  0  8  8  0  0  0  0  0  8  0  8  8  0  8  8  8  8  0  0  8  8  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  8  8  0  8  0  8  8  0  0  8  8  8  8  8  0  8  0  0  0  0  8  0  0
 0  0  0  0  0  0  0  8  0  8  8  8  0  8  8  0  0  0  8  8  8  8  0  8  8  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+129x^28+144x^30+714x^32+2144x^34+699x^36+144x^38+99x^40+19x^44+1x^48+1x^52+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 88.5 seconds.