The generator matrix

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

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+439x^84+770x^86+778x^88+668x^90+504x^92+322x^94+254x^96+180x^98+72x^100+72x^102+31x^104+4x^106+1x^108

The gray image is a linear code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.16 in 3.1 seconds.