The generator matrix

 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  1  1  1  1  1  1 X^3  1  1  1  X  X  1  1  0  1  1 X^3 X^2  1
 0  X  0  X X^3  0 X^3+X  X X^2 X^2+X X^2 X^3+X^2+X X^3+X^2 X^2 X^2+X X^2+X  0 X^3+X X^3+X^2+X X^2 X^3+X^2+X X^3+X X^3 X^3+X^2+X X^3+X^2  0  X X^2 X^3+X^2+X X^3+X X^2  X  X X^3 X^3+X^2+X X^2+X  0 X^3+X^2 X^3+X  X X^3+X^2+X X^3  X X^2 X^3
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^3  X X^3+X  0 X^2+X X^3+X^2+X X^3+X^2  0 X^3+X^2+X X^2 X^3 X^3 X^3+X^2  X X^2+X X^2 X^2 X^3 X^3+X X^3+X X^3+X^2+X X^2+X  X X^3+X X^2+X X^2  0 X^3+X X^3+X X^3+X X^2+X X^3+X^2+X X^3+X^2+X X^2  X  0
 0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0 X^3 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+120x^41+139x^42+222x^43+369x^44+442x^45+326x^46+194x^47+83x^48+70x^49+31x^50+32x^51+10x^52+8x^53+1x^76

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 0.11 seconds.