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

generates a code of length 84 over Z16 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+111x^76+310x^77+570x^78+842x^79+992x^80+1178x^81+1579x^82+1940x^83+1979x^84+1720x^85+1452x^86+1122x^87+778x^88+652x^89+394x^90+256x^91+192x^92+114x^93+93x^94+40x^95+39x^96+10x^97+5x^98+8x^99+4x^100+2x^102+1x^118

The gray image is a code over GF(2) with n=672, k=14 and d=304.
This code was found by Heurico 1.16 in 7.03 seconds.