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

generates a code of length 83 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+414x^78+96x^79+443x^80+372x^81+512x^82+592x^83+388x^84+392x^85+466x^86+80x^87+189x^88+4x^89+68x^90+64x^92+12x^94+2x^96+1x^136

The gray image is a code over GF(2) with n=664, k=12 and d=312.
This code was found by Heurico 1.16 in 35.4 seconds.