The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+209x^28+216x^29+776x^30+1088x^31+1835x^32+2808x^33+2574x^34+2784x^35+1888x^36+1064x^37+654x^38+224x^39+210x^40+8x^41+26x^42+15x^44+2x^46+2x^48

The gray image is a code over GF(2) with n=272, k=14 and d=112.
This code was found by Heurico 1.16 in 2.2 seconds.