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

generates a code of length 91 over Z16 who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+62x^80+32x^81+96x^82+84x^83+155x^84+152x^85+283x^86+252x^87+830x^88+324x^89+1672x^90+372x^91+1670x^92+340x^93+856x^94+228x^95+251x^96+140x^97+99x^98+72x^99+69x^100+36x^101+36x^102+16x^103+19x^104+18x^106+8x^108+6x^110+4x^112+3x^114+2x^116+2x^118+1x^120+1x^134

The gray image is a code over GF(2) with n=728, k=13 and d=320.
This code was found by Heurico 1.16 in 3.7 seconds.