The generator matrix

 1  0  0  1  1  1  0  1  1 X^2  1  X  1 X^2+X  1  X X^2+X  1  1 X^2  1  1  X  0  1  1 X^2+X  1  X  1  0  1 X^2  1 X^2  1  0  0  1  1  1  0  1  1  1 X^2 X^2+X  1  1  X  1  X X^2+X  1  0  X X^2+X  1  X  1  1  1  1  X  1 X^2+X  1 X^2+X X^2  1  1  1 X^2  X  0  1  1  1 X^2+X X^2  0  1  1 X^2+X X^2+X X^2+X  1 X^2+X  1  1
 0  1  0  0  1  1  1 X^2  1  1 X+1 X^2+X  X  1 X^2+X  1  1  1  0  X X^2+X+1 X+1  1 X^2 X^2 X^2+X  1 X^2+X+1 X^2 X^2+X  1 X^2+1  1 X^2+X  1 X+1 X^2+X  1  0  0  0  1 X^2+X+1  0 X^2+1  1  1 X^2+X+1  X  1  0  1  X  1  X  1  0 X^2+X+1  1  X X^2+1  X X^2+X+1  1  X X^2  X  1  1 X^2+1 X+1  1  1  1  0 X^2+X+1 X^2+X X+1  X X^2  1 X^2+X  X  1  1  1  X  1 X^2+X+1  0
 0  0  1 X+1 X^2+X+1  0 X+1  X  1  X  0  1  1  1  X X^2+X X+1 X^2+X  1  1  1 X+1  1  1  0 X+1 X^2 X^2+X  1 X^2+X X^2+1 X^2  X X^2  0 X^2+1  1 X^2 X+1 X+1 X^2+1 X+1 X^2+X X^2+X X+1  1 X^2+X+1 X^2 X+1  X  1  0  1  1  1 X^2+X  1 X^2+1  1 X^2+X+1 X^2 X^2 X+1  0 X^2+X  1 X^2+1 X^2+1 X^2+X X^2+1 X^2 X+1 X^2+1  0  1 X^2+X+1 X^2+X X+1  1  1  0 X^2+X X^2+X X^2+X X^2+X X+1 X+1 X^2+X+1  1  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 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 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2  0 X^2
 0  0  0  0 X^2  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  0  0  0 X^2  0 X^2 X^2  0 X^2  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  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  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  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0
 0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 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+192x^82+316x^83+448x^84+492x^85+646x^86+716x^87+566x^88+660x^89+605x^90+600x^91+555x^92+500x^93+445x^94+400x^95+310x^96+236x^97+172x^98+124x^99+79x^100+32x^101+38x^102+20x^103+16x^104+7x^106+5x^108+7x^110+3x^112+1x^116

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 10.2 seconds.