The generator matrix

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

generates a code of length 45 over Z2[X]/(X^3) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+289x^40+304x^41+494x^42+360x^43+657x^44+340x^45+368x^46+248x^47+394x^48+160x^49+238x^50+96x^51+95x^52+28x^53+20x^54+4x^56

The gray image is a linear code over GF(2) with n=180, k=12 and d=80.
This code was found by Heurico 1.16 in 14.1 seconds.