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

generates a code of length 89 over Z16 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+38x^77+77x^78+184x^79+269x^80+318x^81+645x^82+806x^83+1508x^84+1434x^85+3144x^86+2020x^87+4680x^88+2574x^89+4629x^90+2308x^91+3131x^92+1378x^93+1491x^94+640x^95+520x^96+338x^97+182x^98+158x^99+86x^100+62x^101+51x^102+20x^103+30x^104+2x^105+14x^106+8x^107+11x^108+4x^110+4x^112+1x^114+1x^118+1x^122

The gray image is a code over GF(2) with n=712, k=15 and d=308.
This code was found by Heurico 1.16 in 42.7 seconds.