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

generates a code of length 86 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+142x^77+395x^78+770x^79+959x^80+1460x^81+2026x^82+2536x^83+2921x^84+3574x^85+3501x^86+3804x^87+3014x^88+2380x^89+1606x^90+1224x^91+872x^92+668x^93+378x^94+222x^95+113x^96+72x^97+62x^98+32x^99+20x^100+4x^101+4x^103+3x^104+4x^105+1x^116

The gray image is a code over GF(2) with n=688, k=15 and d=308.
This code was found by Heurico 1.16 in 26.7 seconds.