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  X  X  X  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2  0  0  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3 X^3  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0
 0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0
 0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0
 0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+16x^40+36x^41+23x^42+92x^43+26x^44+584x^45+155x^46+24x^47+15x^48+20x^49+12x^50+12x^51+6x^52+1x^54+1x^82

The gray image is a linear code over GF(2) with n=360, k=10 and d=160.
This code was found by Heurico 1.16 in 0.079 seconds.