The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+208x^82+216x^83+601x^84+404x^85+718x^86+504x^87+813x^88+460x^89+821x^90+456x^91+696x^92+476x^93+451x^94+272x^95+352x^96+180x^97+219x^98+80x^99+132x^100+16x^101+61x^102+8x^103+22x^104+12x^106+7x^108+6x^110

The gray image is a linear code over GF(2) with n=360, k=13 and d=164.
This code was found by Heurico 1.16 in 5.14 seconds.