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

generates a code of length 85 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+163x^78+156x^80+40x^81+310x^82+256x^83+714x^84+944x^85+701x^86+256x^87+235x^88+40x^89+105x^90+61x^92+50x^94+36x^96+13x^98+12x^100+2x^102+1x^148

The gray image is a code over GF(2) with n=680, k=12 and d=312.
This code was found by Heurico 1.16 in 36.1 seconds.