The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+194x^28+796x^29+1984x^30+4198x^31+7513x^32+11596x^33+12758x^34+11780x^35+7804x^36+4190x^37+1772x^38+622x^39+194x^40+88x^41+30x^42+8x^43+6x^44+2x^45

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 16.9 seconds.