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

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+152x^41+150x^42+200x^43+364x^44+340x^45+404x^46+196x^47+49x^48+112x^49+54x^50+16x^51+4x^53+4x^55+1x^56+1x^72

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 113 seconds.