The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+87x^80+44x^81+272x^82+228x^83+384x^84+508x^85+520x^86+504x^87+561x^88+800x^89+591x^90+680x^91+544x^92+688x^93+457x^94+320x^95+329x^96+244x^97+149x^98+52x^99+97x^100+20x^101+36x^102+8x^103+27x^104+11x^106+13x^108+11x^110+3x^112+1x^114+1x^116+1x^124

The gray image is a linear code over GF(2) with n=360, k=13 and d=160.
This code was found by Heurico 1.16 in 6.43 seconds.