The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+177x^28+308x^29+1172x^30+1940x^31+4774x^32+6900x^33+11663x^34+11316x^35+12095x^36+7100x^37+4747x^38+1820x^39+931x^40+284x^41+205x^42+28x^43+68x^44+5x^46+2x^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 22.1 seconds.