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

generates a code of length 98 over Z16 who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+43x^86+88x^87+195x^88+228x^89+523x^90+418x^91+1148x^92+856x^93+2380x^94+1520x^95+4275x^96+2002x^97+5431x^98+2136x^99+4412x^100+1548x^101+2365x^102+740x^103+1002x^104+366x^105+421x^106+164x^107+174x^108+86x^109+71x^110+42x^111+34x^112+20x^113+23x^114+10x^115+18x^116+14x^117+4x^118+2x^119+5x^120+2x^122+1x^142

The gray image is a code over GF(2) with n=784, k=15 and d=344.
This code was found by Heurico 1.16 in 39.2 seconds.