The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1 X^2 X^3  1  1  1  1 X^2  1  1  1  X  1 X^3+X^2  X  1  0 X^2  1  0  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2 X^3+X^2 X^2+X  0 X^3  X X^3+X^2 X^3+X^2+X X^2  X X^2+X X^2+X X^2+X X^3+X^2  X  X X^3+X X^2 X^2+X X^2+X  X X^2 X^2  0  X X^3  X  0
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^2+X  X X^3+X  X  0 X^3+X^2 X^3+X  X X^2 X^3+X^2 X^2+X  X X^3+X X^3 X^2+X  0  0 X^2 X^2 X^3+X^2+X X^2+X X^2+X  X X^3+X^2+X X^3+X^2+X X^3+X  X X^3+X^2+X X^2+X X^2+X  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  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+77x^40+208x^41+382x^42+452x^43+687x^44+706x^45+607x^46+344x^47+287x^48+136x^49+92x^50+48x^51+34x^52+22x^53+7x^54+4x^55+1x^56+1x^68

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.