The generator matrix

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

generates a code of length 35 over Z16 who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+100x^27+371x^28+772x^29+1206x^30+2378x^31+3871x^32+7690x^33+9703x^34+12778x^35+10241x^36+8030x^37+3939x^38+2258x^39+1007x^40+646x^41+301x^42+146x^43+56x^44+14x^45+19x^46+4x^47+5x^48

The gray image is a code over GF(2) with n=280, k=16 and d=108.
This code was found by Heurico 1.16 in 29.9 seconds.