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  X  1  1  1  1  1  1  1 X^3  1  1  1  1  X  X  X
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3 X^2  0 X^2 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2  0  0 X^3+X^2 X^3 X^3  0 X^3  0 X^3 X^3+X^2  0 X^3
 0  0 X^3  0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0  0
 0  0  0 X^3  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  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3
 0  0  0  0  0  0 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  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+153x^40+978x^44+640x^46+212x^48+54x^52+9x^56+1x^80

The gray image is a linear code over GF(2) with n=360, k=11 and d=160.
This code was found by Heurico 1.16 in 44.5 seconds.