The generator matrix

 1  0  1  1  1  6  1  1 12  1  1 10  1  0  1  1  1  6  1  1  1 10  1  1  1 12  0  1  6  1  1  1 12  2
 0  1  3  6  5  1 12 15  1 10  9  1  0  1  3  6  5  1 12 10  9  1  0  9 15  1  1  3  1  6  5  5  2  0
 0  0  8  0  0  0  0  0  0  8  8  0  8  0  0  0  8  8  8  0  8  8  0  0  8  0  8  8  8  8  8  8  0  0
 0  0  0  8  0  0  0  8  0  8  8  0  0  8  8  0  8  8  0  0  0  0  8  8  8  8  8  0  0  8  8  8  0  0
 0  0  0  0  8  0  0  0  8  0  8  0  8  8  8  8  8  0  8  0  0  8  8  0  0  0  0  8  0  8  0  8  0  0
 0  0  0  0  0  8  0  8  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  8  8  0  8  0  8  8  8  0  0
 0  0  0  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  8  8  0  0  0  0  8  0  8  0  0  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+70x^28+24x^29+265x^30+472x^31+1085x^32+1296x^33+1768x^34+1296x^35+1102x^36+472x^37+252x^38+24x^39+42x^40+16x^42+4x^44+1x^46+2x^54

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 0.369 seconds.