The generator matrix

 1  0  0  1  1  1  2  4  1  1  0 14  1  1  1  4  1 14  2  1  1  6  1  1  1  1 12  0  2  8 12  1  1  6
 0  1  0  2  1 11  1  6 14  9  1  1 15  6  7  1  8  1 10  4  5  1  1  0 15  2  1 14  1  1  6 10  9  1
 0  0  1  1  3  4  5  1  6  2  9  0  5  3 14  2  6 15  1  3  0  5 13 10  7  2  1  1  7  4  1  3 11  2
 0  0  0  4  0  0 12 12  4 12  8  4 12 12  8 12  8  0  0  4 12  4 12 12 12  0  0  8 12 12 12  8 12  4
 0  0  0  0  4  8  8  8  8  0  0  0  4  4  8 12 12  0  4  8 12  4  4  8  0  4 12 12  0  8  0 12 12  0

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

Homogenous weight enumerator: w(x)=1x^0+230x^28+700x^29+1896x^30+4312x^31+7713x^32+11672x^33+12598x^34+11508x^35+7786x^36+4444x^37+1746x^38+624x^39+230x^40+16x^41+42x^42+4x^43+8x^44+6x^46

The gray image is a code over GF(2) with n=272, k=16 and d=112.
This code was found by Heurico 1.16 in 17.4 seconds.