The generator matrix

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

generates a code of length 45 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+11x^42+76x^43+21x^44+304x^45+17x^46+64x^47+9x^48+3x^50+4x^51+1x^52+1x^78

The gray image is a linear code over GF(2) with n=360, k=9 and d=168.
This code was found by Heurico 1.16 in 0.063 seconds.