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

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+101x^80+4x^81+364x^82+40x^83+531x^84+128x^85+576x^86+232x^87+768x^88+376x^89+846x^90+472x^91+878x^92+400x^93+660x^94+248x^95+499x^96+100x^97+364x^98+32x^99+232x^100+16x^101+144x^102+90x^104+50x^106+30x^108+4x^110+5x^112+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 8.77 seconds.