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

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+89x^40+134x^42+160x^43+141x^44+64x^45+156x^46+32x^47+153x^48+38x^50+27x^52+24x^54+4x^56+1x^80

The gray image is a linear code over GF(2) with n=180, k=10 and d=80.
This code was found by Heurico 1.16 in 0.102 seconds.