The generator matrix

 1  0  1  1  1 14  1  1  4  1  1 10  1  1  2  1  6  1  1  1  0  1 12  1 10 10  1 12  1 12  1  1  1  1  1  1  1 10 12  1  1  1  1  1  4  0  1  6  1  1  2  1  2  1  1  1  1  1  1 12  4 10  1  1 10  1  1  8  8  1  0  6  8  0  1  6  1  1  4  1  1  1  2  1
 0  1  1  6  3  1 13  4  1 10  3  1 15  8  1  2  1  1 12 13  1  6  1 15  1  1 11  1  5  1  0 14  2 12 15  1  3  1  1  0 12  5 14 13  1  1 11  1  5 12  1 11  1  6  2 13 11  6  6  4  1  1  7 15  1  4  1  1  2  9  1  1  1  1 11  1  9  6  1 10  5 13 14  0
 0  0  2  0  8  0  8 10 14 10  2 14  0  2  8  8  6  0  8 10  8  2 14 10 10 12 12 12 12  2 12  4  2 10 14  6 14 10  6  6  4  2 14  0 12 10  8  4 14  0  4  6  0  6  4  4  8  0 14  2  0  4  2 14  2 12  4 10 14 14  6  2  4  0 12 10  8 10 10  4  2  6  6  8
 0  0  0 12  0 12 12  0 12  4  4  0  8  8  4  4  8  4  8  8  8 12  4 12  0  4  0  0 12  4  4  0  8  4 12  0  0  4  8 12 12  4 12  8  4 12 12  0 12 12 12  8  8  0 12  8  4  8  8  8 12  0  0  4  8  8 12  0 12  8  0  4  8 12  4 12  0  8  0  8  0 12  4  0

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

Homogenous weight enumerator: w(x)=1x^0+72x^78+402x^79+645x^80+808x^81+951x^82+946x^83+984x^84+790x^85+776x^86+774x^87+427x^88+256x^89+175x^90+74x^91+22x^92+26x^93+24x^94+12x^95+14x^96+8x^97+2x^100+1x^104+1x^106+1x^114

The gray image is a code over GF(2) with n=672, k=13 and d=312.
This code was found by Heurico 1.16 in 1.66 seconds.