The generator matrix

 1  0  1  1  1 X^3+X^2+X  X  1  1 X^3+X^2  1  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X  1  1 X^2  1  1  1  1  X  1  1  1  X  0 X^3  1  1  1 X^3+X^2+X  X  1  1 X^2 X^3  1
 0  1 X+1 X^2+X X^3+X^2+1  1  1 X^3+X^2 X^2+X+1  1 X^3+X^2+X X^2+1  X X^3+1  1 X^3 X+1  1 X^2 X^3+X^2+X+1  1 X^3+X  1  1  0 X^2+X X^3 X^3+X^2+X X^3+X^2 X^3 X^3+X X^3 X^3+X^2+X  1  1  1 X^3+X^2+1 X^2+1  1 X^3+X^2 X^3+X X^3+X^2+X+1  1  X  0
 0  0 X^2  0 X^3+X^2 X^2 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3  0 X^2 X^3 X^2 X^3+X^2 X^3  0  0 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^2 X^2 X^2  0 X^2 X^3  0 X^3  0  0  0
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3  0  0  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+55x^40+204x^41+290x^42+680x^43+437x^44+900x^45+432x^46+544x^47+252x^48+172x^49+40x^50+52x^51+23x^52+4x^53+6x^58+4x^59

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 0.203 seconds.