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  1  2  1  1  1  1  1  1  2  1  1  4  1  1  1  2  1  4  1  1  1  2  1  2  1  1  1  0  1  1  8  1  1  2  1  2  4  0  1  2  1  1  1  4  2  1  2  2  4  1  1  1
 0 12  0  0  0  0  0  0  0  4 12 12  4  4  8 12 12  0  8 12  4 12  0 12  8  4  0 12  4 12  8  0  8  4  4 12  4  4  0  8  8  8  0 12  8  8  0  8 12  8 12 12 12  4  0  0 12  4  8  0 12  8  8 12  8 12  8 12  8  4  8  4 12  0  8 12 12 12  8  0  8  4 12 12  0  0
 0  0 12  0  0  0  4 12 12  4  4  0  8  4  0 12  8  8  4  8  4  8  4  0  4  0 12  4  4 12  0  8  0  4  4  8  0 12  0  4  0  8  4  8  4  4  4  8 12  8 12  8 12 12  4 12  4  4  4  4  8  0  0  4  4 12  0  8 12  0 12 12 12  4  8  0 12  4  4 12  8  4  0  4  0  4
 0  0  0 12  0  4  4  4  0  8  0  8 12  4  0  4 12  8 12  8 12 12  0  0  8 12 12  0  0 12  4 12 12  0  0  0  8  4 12  4  8 12  8  4  8  4 12  0  0  0 12 12  0  4 12 12  4  4  4  8  4  4  8  0  0  8 12  4  4 12 12  4  0  0  8  4 12  4  8  0 12 12  8 12 12 12
 0  0  0  0 12  4  8  4  4  0  4  4  0  4  8  8  4 12 12  8  4  4  0 12  4  8  0  8  4  8  8  4 12  8 12  0 12  8  8  4 12 12  4  0 12 12  0  0 12  4  8 12  4 12  4  8 12  4  8  4 12  0  8  0  4  4  8  4  8  0  0  8  0  8  8 12 12  4  4  8 12  0  0 12  8  4
 0  0  0  0  0  8  8  0  8  8  8  0  8  0  8  0  0  8  8  8  8  8  8  8  0  0  0  0  0  8  8  0  8  8  0  0  0  8  8  8  0  0  8  8  8  0  0  8  0  0  0  8  8  8  0  0  8  8  8  0  8  0  0  0  8  8  0  0  0  8  8  0  8  0  8  8  8  8  8  8  8  0  8  0  0  8

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

Homogenous weight enumerator: w(x)=1x^0+72x^77+124x^78+132x^79+235x^80+152x^81+559x^82+452x^83+1000x^84+756x^85+1399x^86+870x^87+987x^88+310x^89+469x^90+118x^91+161x^92+54x^93+97x^94+62x^95+25x^96+58x^97+32x^98+30x^99+18x^100+6x^101+8x^102+4x^104+1x^132

The gray image is a code over GF(2) with n=688, k=13 and d=308.
This code was found by Heurico 1.16 in 93.4 seconds.