The generator matrix

 1  0  1  1  1  4  1  1  0  1  1 10 10  1  1  1  1  1  0  1  1  6  0  1  1  4  1  4  1 14  1  1  1  1
 0  1  1  0  3  1  1 12  1  3  8  1  1  7  6 13 14  2  1  5 14  1  1  7  1  1  6  4 15  1 10 15 11  0
 0  0  2  0  0  8 10 14  2 12  2  2  4 14 14 12  8  0 14 12  6  4  6  0  0 14 12  0  2 14  0  8 12  4
 0  0  0  2  0 10 14  8  2  2 14  4 10  4  0 14  2  4  8 10 12  0  6 10  8 12  4  2  6 10 14  4 12  4
 0  0  0  0  8  0  0  8  8  8  8  0  8  8  0  0  8  8  8  8  8  8  0  0  0  0  0  8  0  8  8  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+97x^28+464x^29+892x^30+2198x^31+3680x^32+5922x^33+6082x^34+6388x^35+3622x^36+1950x^37+845x^38+414x^39+113x^40+62x^41+20x^42+8x^43+7x^44+2x^45+1x^46

The gray image is a code over GF(2) with n=272, k=15 and d=112.
This code was found by Heurico 1.16 in 5.49 seconds.