The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+84x^41+213x^42+164x^43+508x^44+172x^45+472x^46+136x^47+191x^48+60x^49+18x^50+20x^51+2x^52+4x^53+1x^58+2x^60

The gray image is a linear code over GF(2) with n=360, k=11 and d=164.
This code was found by Heurico 1.16 in 0.078 seconds.