The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  4  1  1  1  0  2  1  1  1  1  4  2  1  4  1  1  2  8  1  1  1
 0 12  0  0  0  0  0  0  0  4 12 12  4 12  4 12  8 12  8 12  0  8 12  8  4 12  8  4  0  4 12  8  8  0  0  4  4  8  8  8  0 12  8 12  8  4  4  4 12 12  0 12  0  8 12  4  4 12 12  4  8  4  8  0  0  0  8 12  8  4  0  8  4 12  0  8  4  8  0 12  4  0  4  8 12  0
 0  0 12  0  0  8 12 12  4  4  4  8  4 12  0  8  0  8  0  4  4  4  4  4 12  0 12  4  8  0  8  0  0  4  4 12 12  4  4 12 12 12  0  8  0 12  4  0  4  4  8  4 12  8  4  8  8 12  0  0 12  8 12  8  4 12  0 12 12  0 12  8 12  4  4 12  0  8  8  8  8 12  0 12  0  0
 0  0  0 12  0 12 12  4  8  0  0  0  4 12  4  4  8 12  4  4  8  8  4  4  0  8  4  8  0  0  4 12 12 12  0  0 12  8  0 12  4  8  4  0 12  0  0  4  8 12  0  4  8  8  0 12  8 12 12 12 12  8  0  4 12  8 12  8  8  0  8 12  8 12  0  8  4 12 12  8  0  4 12  0 12  4
 0  0  0  0 12  4  8  4  4  0  4  4  4  0  8 12 12  8  8  4  8 12  0 12  4 12  0  0  8  0  4  4  0  8  4  0  4  0  8 12  4  4  4 12 12  8 12 12  8  0  0 12  8 12  0  0 12  8  4  8  0  0  4  8 12  0  8  8  4  8 12 12 12  4 12 12  0  4  4  8  8 12  0 12 12 12

generates a code of length 86 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+42x^78+76x^79+95x^80+92x^81+144x^82+184x^83+664x^84+174x^85+1227x^86+232x^87+644x^88+108x^89+142x^90+82x^91+38x^92+28x^93+32x^94+26x^95+20x^96+4x^97+9x^98+6x^99+10x^100+6x^101+3x^102+2x^103+4x^105+1x^146

The gray image is a code over GF(2) with n=688, k=12 and d=312.
This code was found by Heurico 1.16 in 1.04 seconds.