The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+219x^78+800x^79+1295x^80+1774x^81+1731x^82+1940x^83+1617x^84+2008x^85+1403x^86+1272x^87+884x^88+626x^89+363x^90+162x^91+97x^92+88x^93+56x^94+32x^95+10x^96+3x^98+2x^99+1x^106

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 3.62 seconds.