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

generates a code of length 91 over Z16 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+125x^78+403x^80+32x^81+578x^82+104x^83+957x^84+460x^85+1556x^86+1160x^87+2833x^88+2576x^89+3827x^90+3632x^91+3936x^92+2568x^93+2893x^94+1136x^95+1365x^96+496x^97+868x^98+104x^99+512x^100+12x^101+310x^102+8x^103+184x^104+71x^106+32x^108+12x^110+11x^112+3x^116+3x^120

The gray image is a code over GF(2) with n=728, k=15 and d=312.
This code was found by Heurico 1.16 in 44.7 seconds.