The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+160x^28+392x^30+128x^31+1457x^32+896x^33+2160x^34+896x^35+1429x^36+128x^37+392x^38+128x^40+18x^44+6x^48+1x^52

The gray image is a code over GF(2) with n=272, k=13 and d=112.
This code was found by Heurico 1.16 in 24.2 seconds.