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

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

Homogenous weight enumerator: w(x)=1x^0+58x^78+106x^79+172x^80+286x^81+354x^82+464x^83+570x^84+682x^85+1002x^86+1460x^87+2341x^88+3138x^89+3820x^90+4152x^91+3775x^92+3120x^93+2219x^94+1554x^95+913x^96+678x^97+510x^98+316x^99+284x^100+222x^101+172x^102+108x^103+121x^104+58x^105+49x^106+28x^107+11x^108+8x^109+5x^110+4x^111+4x^112+2x^114+1x^122

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 44.3 seconds.