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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+158x^78+160x^79+221x^80+316x^81+494x^82+480x^83+576x^84+492x^85+294x^86+384x^87+132x^88+212x^89+114x^90+24x^92+4x^93+28x^94+5x^96+1x^144

The gray image is a code over GF(2) with n=672, k=12 and d=312.
This code was found by Heurico 1.16 in 19.6 seconds.