The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+295x^84+256x^86+367x^88+240x^90+375x^92+256x^94+213x^96+16x^98+18x^100+1x^104+5x^108+3x^116+2x^128

The gray image is a linear code over GF(2) with n=360, k=11 and d=168.
This code was found by Heurico 1.16 in 62.8 seconds.