The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+198x^28+364x^29+936x^30+2176x^31+3781x^32+8036x^33+10528x^34+13624x^35+10324x^36+8084x^37+3900x^38+2224x^39+796x^40+284x^41+184x^42+24x^43+62x^44+4x^46+6x^48

The gray image is a code over GF(2) with n=280, k=16 and d=112.
This code was found by Heurico 1.16 in 21.4 seconds.