The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+34x^41+32x^42+36x^43+102x^44+122x^45+92x^46+40x^47+19x^48+14x^49+4x^50+4x^51+5x^52+6x^53+1x^84

The gray image is a linear code over GF(2) with n=180, k=9 and d=82.
This code was found by Heurico 1.16 in 68.8 seconds.