The generator matrix

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

generates a code of length 90 over Z2[X]/(X^3) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+248x^86+222x^88+224x^90+118x^92+124x^94+40x^96+24x^98+1x^100+16x^102+1x^112+1x^116+4x^118

The gray image is a linear code over GF(2) with n=360, k=10 and d=172.
This code was found by Heurico 1.16 in 13.4 seconds.