The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  X  1  1  1  1  0  1 X^2+X  1  1  1  X  1  1 X^2  1  X X^2+X  1  1  1  1  1  1  0  1  X  1  1  0  1 X^2  1  1  X X^2+X  1  1  1  1  1  1  1  0  0  1  X  1 X^2+X  1  0  0  1  1  1  1  1  1  1  1  1  X X^2+X  1  1 X^2  X  1  X X^2  1  X  1  X  X  1  1  1  1  1  1
 0  1  1  0 X^2+X+1  1  X X+1  1  1 X^2+X+1 X^2 X^2+X  1  1  X  1  0 X+1  1  1  X X^2+1  1 X+1  1  1  X X^2+1  0 X^2+X X^2+1 X+1  1 X^2  1 X^2+X+1  1  1  X  1 X^2+X+1  X  1  1 X^2+X+1  X X^2+X X+1  0 X^2+X+1 X^2+1  1  1  X  1  1  1 X^2+X  1  1 X+1  0  0 X^2  X X+1  1  X X^2+X  1  1 X^2+X X^2+1  1  1  X X^2 X^2  0 X^2 X^2+X  1  1 X^2+1 X^2+X+1  1  1 X^2  0
 0  0  X  0 X^2+X  0  0  0 X^2 X^2 X^2  X X^2+X X^2+X  X X^2+X  X X^2+X X^2+X X^2 X^2+X X^2 X^2  X X^2+X X^2+X  0 X^2  0 X^2 X^2+X  X X^2 X^2+X X^2  X X^2  0  X  0  0 X^2+X  X X^2+X X^2  0  0  0 X^2 X^2+X  X  X  0 X^2  0  X X^2  0 X^2+X X^2  0  0  X X^2+X X^2+X  X  0 X^2  0 X^2+X X^2+X  X X^2  X  X X^2  0  X  0  X  X X^2+X X^2+X X^2 X^2  X X^2+X X^2 X^2+X  0
 0  0  0  X  0  0  X X^2 X^2+X  X  X  0 X^2+X  X  X X^2  X  X X^2+X X^2  0  0  X  0 X^2 X^2+X  X  X  0 X^2  X X^2+X X^2  X  X X^2 X^2+X X^2+X X^2  0  X  X X^2  0  X  X X^2 X^2 X^2 X^2+X  0 X^2+X  X  0  0  X X^2  0 X^2  0  0 X^2+X X^2+X  0 X^2  X  X X^2+X  X  X X^2+X  X  X  0  X X^2+X  0 X^2  X  0  0  X  0 X^2+X X^2+X X^2  0  X  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 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  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2  0  0  0  0  0 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  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  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+35x^80+90x^81+170x^82+338x^83+323x^84+640x^85+383x^86+772x^87+457x^88+796x^89+485x^90+758x^91+408x^92+806x^93+334x^94+486x^95+215x^96+220x^97+116x^98+114x^99+65x^100+52x^101+31x^102+20x^103+27x^104+12x^105+11x^106+6x^107+4x^108+6x^109+2x^110+2x^111+1x^112+2x^113+2x^114+2x^118

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 6.32 seconds.