The generator matrix

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

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+112x^40+152x^41+332x^42+342x^43+923x^44+604x^45+772x^46+306x^47+237x^48+76x^49+137x^50+38x^51+39x^52+16x^53+6x^54+2x^55+1x^74

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 0.25 seconds.