The generator matrix

 1  0  1  1  1  6  1  1  8  1  1 14  1  4  1  6  1  1  8  1 10  1  1  1  1  1  1  2  8  2  1  8  8  2
 0  1 11  6  1  1  8 11  1 13  6  1 10  1 11  1  8  5  1  8  1 13  4  9 15  8 15  1  1 14 12  1  2 14
 0  0 12  0  0  0  0  0  8  4  4  4  4  8  4  0  8  0  4 12 12 12  8  8  4 12 12  0  8  4 12 12  0  0
 0  0  0 12  0  0 12  8 12  0  0 12  0  4  4 12  8  0  8  8 12 12  0  8 12  4 12 12  8  0  0 12  4  8
 0  0  0  0  4  0  8  4  0  8  4 12 12  0  4  4 12  8  8  0  8  4  4  8  8 12  8  8 12  8 12 12  0 12
 0  0  0  0  0  8  8  8  0  8  8  8  0  8  0  8  8  8  8  8  0  8  0  0  8  0  0  8  8  0  8  8  8  0

generates a code of length 34 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+80x^27+200x^28+362x^29+924x^30+1758x^31+4446x^32+5010x^33+7358x^34+4914x^35+4401x^36+1778x^37+864x^38+338x^39+185x^40+78x^41+38x^42+14x^43+15x^44+4x^45

The gray image is a code over GF(2) with n=272, k=15 and d=108.
This code was found by Heurico 1.16 in 12.8 seconds.