The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+458x^78+624x^79+1541x^80+1272x^81+1914x^82+1720x^83+1987x^84+1664x^85+1614x^86+1264x^87+935x^88+584x^89+394x^90+40x^91+219x^92+88x^94+42x^96+12x^98+9x^100+1x^104+1x^108

The gray image is a code over GF(2) with n=672, k=14 and d=312.
This code was found by Heurico 1.16 in 30.4 seconds.