The generator matrix

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

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+169x^40+140x^41+350x^42+496x^43+682x^44+520x^45+618x^46+496x^47+323x^48+140x^49+104x^50+29x^52+10x^54+10x^56+6x^58+1x^60+1x^64

The gray image is a linear code over GF(2) with n=360, k=12 and d=160.
This code was found by Heurico 1.16 in 0.313 seconds.