The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  8  1  1  2  1  0  4  2  2 12  1  1  1  2  2  1  1  2  2  4
 0  2  0  6  4 14 12  2  0  8  6  6  2 12 14  2 10  4  6  8  2  2 10  6  2  6 10  4  2 14  0  8  4  4  8
 0  0 12  0  4  4  0  4  0  4  0 12  4  8  4 12  8 12  0 12  8  4  8  8  8  8  8 12 12  4  0  8  4  4  4
 0  0  0  8  0  0  0  0  0  0  0  8  8  8  0  0  0  0  8  8  8  8  8  0  0  8  0  0  8  8  0  0  8  8  0
 0  0  0  0  8  0  0  0  0  0  8  8  0  0  8  8  8  8  0  0  0  0  0  0  8  8  8  8  0  8  8  0  0  8  0
 0  0  0  0  0  8  0  0  8  8  0  8  0  0  0  0  0  8  8  8  0  8  0  0  8  0  8  8  0  8  8  8  8  0  8
 0  0  0  0  0  0  8  0  0  0  0  0  0  8  8  0  8  8  8  8  0  8  0  8  0  8  0  8  8  0  8  8  8  8  0
 0  0  0  0  0  0  0  8  8  8  0  0  8  0  8  8  0  8  8  8  0  0  8  8  8  8  0  0  0  8  0  0  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+158x^28+56x^29+462x^30+432x^31+1101x^32+1992x^33+2612x^34+3232x^35+1956x^36+1992x^37+1296x^38+432x^39+440x^40+56x^41+108x^42+46x^44+2x^46+10x^48

The gray image is a code over GF(2) with n=280, k=14 and d=112.
This code was found by Heurico 1.16 in 2.57 seconds.