The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1  1  1  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X X^2 X^2+X  0 X^2+X  0 X^2+X  0 X^2+X X^2  X X^2  X  X X^2  0  0 X^2+X X^2+X  0  0 X^2 X^2 X^2+X X^2+X  X  X X^2  0  0 X^2 X^2 X^2+X X^2+X  X  X  0  0 X^2  0
 0  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 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+17x^40+48x^42+210x^44+176x^46+21x^48+32x^50+6x^52+1x^88

The gray image is a linear code over GF(2) with n=180, k=9 and d=80.
This code was found by Heurico 1.16 in 0.0527 seconds.