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 X^2  X  0  X  1  1 X^2  X X^2  1  1  X  X  1  0  1  1  1  1 X^2  1 X^2  1  1  0  1  X  1  1  1  1  X  1  1  X  1  X  1  0  1  X  X  0  X  1  X  1  1  0  0  1
 0  X  0  0  0  0  0  0 X^2 X^2  X X^2+X  X  0  0 X^2 X^2+X X^2+X  X  X  X  X  0  X X^2+X  X  0  X X^2+X X^2 X^2+X X^2 X^2 X^2+X  X  0  0  X X^2  0  X  X  0 X^2+X  X X^2  X X^2  X X^2 X^2+X X^2+X  X  X  X  X  0  0  X X^2  X X^2 X^2+X  X  X  0  0 X^2  0 X^2+X X^2 X^2+X  0  X  0 X^2+X X^2+X  X  X  X  0  X  X  X X^2+X X^2+X X^2  X  X  0  0
 0  0  X  0  0  0  0  0  0  0  0  0 X^2 X^2+X X^2+X X^2+X  X X^2+X X^2+X  X X^2 X^2 X^2+X X^2+X  0  0  X  X  X X^2+X X^2+X X^2+X X^2 X^2 X^2+X  X  X X^2 X^2  X X^2+X  0 X^2  X  0 X^2 X^2+X  0 X^2  X X^2 X^2  X  0 X^2  0  0  X  X  X  0  X X^2+X  X  X X^2  0 X^2+X  0 X^2  X  0 X^2  X  X X^2 X^2 X^2 X^2+X X^2  0  X  X X^2+X  0  0  0  0 X^2+X X^2  0
 0  0  0  X  0  0 X^2 X^2+X  X  X  X  X X^2 X^2+X  X X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  X X^2+X  X X^2  X X^2+X X^2+X  X X^2+X  0 X^2  0  0  0 X^2+X X^2+X  X  X X^2+X  X X^2+X X^2 X^2+X  0  X  X X^2+X X^2  X X^2+X X^2+X X^2+X  X X^2  X X^2 X^2 X^2+X X^2+X X^2  X  0 X^2+X X^2+X X^2+X  X X^2+X X^2  0  0  X  X  X X^2 X^2  X X^2  X X^2+X  X X^2+X  0  X X^2 X^2 X^2+X  X X^2
 0  0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  X  X  0 X^2  X  0 X^2+X X^2+X  X X^2+X  X X^2 X^2  X X^2 X^2  0 X^2+X X^2  0 X^2+X  X X^2+X X^2  0 X^2+X  X X^2+X  X X^2+X X^2+X X^2  0 X^2 X^2  0  0 X^2+X  0 X^2  0 X^2+X  X  X X^2+X X^2  0 X^2+X  0  X X^2+X  X X^2+X X^2  X  0  0 X^2 X^2+X X^2 X^2+X  0 X^2+X  X  0 X^2+X  0 X^2 X^2  0 X^2 X^2+X  X  X  X  X  0  X
 0  0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2  X  X  0  X  0 X^2+X X^2+X  0  X X^2 X^2 X^2+X X^2  X X^2+X X^2+X X^2  X X^2 X^2 X^2+X  0  X X^2+X  0  0  0  X  0  X  X X^2+X  0  0  0  0  X  X X^2+X X^2 X^2+X  X X^2+X  0 X^2 X^2+X  X X^2 X^2 X^2+X  0  X X^2+X X^2  0 X^2  X  0 X^2  X X^2  0  0  X  X X^2 X^2  0  X  0 X^2+X X^2  0  0 X^2 X^2+X  X  0  X

generates a code of length 91 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+58x^80+152x^81+176x^82+230x^83+283x^84+342x^85+392x^86+494x^87+564x^88+606x^89+632x^90+590x^91+595x^92+606x^93+562x^94+380x^95+355x^96+312x^97+192x^98+152x^99+136x^100+108x^101+68x^102+60x^103+44x^104+40x^105+24x^106+12x^107+9x^108+8x^109+2x^110+2x^111+2x^112+2x^113+1x^132

The gray image is a linear code over GF(2) with n=364, k=13 and d=160.
This code was found by Heurico 1.16 in 8.78 seconds.