The generator matrix

 1  0  1  1  1  4  1  1  6  1  1  2  1  1 12  4 14 14  1  1  1  8  1  1  0  1  1  0  2  1  1  1 10  2
 0  1  1  4  3  1  2  7  1  6  5  1  8 15  1  1  1  1  5  8  2  1  5 12  1 11 10  1  6  7  6 15  1  4
 0  0  2  2  0  2  2 10  0  0  8  2  4  6  6  4  4  2 14 10 10 12  8 14 14  4  0  6  6  2 14  8  6  2
 0  0  0  8  0  0  0  8  8  0  0  8  8  8  0  0  0  8  8  8  8  8  8  0  0  0  0  0  0  0  8  8  0  0
 0  0  0  0  8  0  0  0  0  0  8  0  0  0  8  8  8  8  8  8  0  0  8  8  8  0  0  8  8  8  8  0  0  8
 0  0  0  0  0  8  0  0  0  8  8  0  0  8  8  0  8  0  0  0  8  8  0  8  8  8  0  0  0  0  8  8  8  0
 0  0  0  0  0  0  8  8  8  0  0  8  8  8  8  8  8  0  0  8  0  8  8  8  0  0  8  0  0  0  0  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+200x^28+344x^29+1072x^30+1872x^31+4186x^32+5448x^33+6524x^34+5504x^35+4202x^36+1864x^37+1004x^38+304x^39+164x^40+24x^41+36x^42+14x^44+4x^46+1x^48

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 5.69 seconds.