The generator matrix

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

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+506x^42+704x^43+786x^44+640x^45+468x^46+376x^47+253x^48+144x^49+142x^50+56x^51+14x^52+4x^54+2x^56

The gray image is a linear code over GF(2) with n=360, k=12 and d=168.
This code was found by Heurico 1.16 in 420 seconds.