The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+53x^28+268x^29+1101x^30+2144x^31+4118x^32+5592x^33+6337x^34+5504x^35+4205x^36+2048x^37+967x^38+272x^39+101x^40+24x^41+11x^42+16x^43+2x^44+4x^45

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 4.38 seconds.