The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  4  1  1  2  1  1  1  4  1  1  2  4  4  4  2  1
 0 12  0  4  0  0  4 12  8 12  0 12  0 12  8 12  4  4  8  4  0  4  8  8  4 12  0 12  4 12 12  4  0  4  0
 0  0 12  4  0 12  4  8  4  4  0  0  0  4  4  8  4 12  4 12  0  4  4  0  8  0 12  8  0  0  8 12 12 12  0
 0  0  0  8  0  0  0  0  0  8  8  0  8  0  8  8  8  0  0  8  0  0  8  8  0  0  0  8  0  8  8  8  8  8  0
 0  0  0  0  8  0  0  8  8  8  8  0  0  8  8  8  0  0  8  0  8  8  0  8  0  0  0  0  0  0  0  8  8  0  0
 0  0  0  0  0  8  0  0  8  0  8  8  0  8  0  0  8  0  8  0  8  0  8  8  0  8  0  8  8  0  0  0  0  8  0
 0  0  0  0  0  0  8  0  0  0  8  0  8  8  8  8  0  8  8  8  8  0  8  0  8  8  8  8  0  0  8  8  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+36x^28+44x^29+84x^30+174x^31+298x^32+328x^33+626x^34+958x^35+614x^36+352x^37+268x^38+138x^39+60x^40+40x^41+36x^42+10x^43+14x^44+4x^45+8x^46+1x^48+2x^50

The gray image is a code over GF(2) with n=280, k=12 and d=112.
This code was found by Heurico 1.16 in 0.221 seconds.