The generator matrix

 1  0  0  1  1  1  2  1  1 14  1  1  4  4  1  0  1  8  1  1  0  1 14  2  1  1  1  8  1  6 12  1  0  4  1
 0  1  0  2 13  7  1  6  9  1  6 11  1  2 12  1  2  1  4  5  4  5  0  1  5  0 15  1  2  1  1  6  1  1  0
 0  0  1  1 11  2  1  0  6  4  7  3  1  1  1  7  6  0  1  5  1  3  1 14 12  5 14  5  2  2  8  4 13  0  0
 0  0  0  4 12  0  8  0  0  0  4  4  8  0 12 12  4  4  8  0 12  8 12  4  0  0  8  8  8 12  8 12  0  4  0
 0  0  0  0  8  0  8  8  8  8  8  8  8  8  8  0  8  8  8  0  8  8  0  0  8  8  8  8  0  0  8  0  0  8  0
 0  0  0  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  8  0  0  0  8  0  8  8  0  8  0  0  0  8  8  0

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

Homogenous weight enumerator: w(x)=1x^0+78x^28+302x^29+839x^30+2034x^31+4439x^32+7512x^33+11314x^34+12470x^35+11322x^36+7760x^37+4364x^38+1854x^39+774x^40+288x^41+118x^42+26x^43+24x^44+10x^45+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 16.9 seconds.