The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+360x^42+152x^43+768x^44+368x^45+888x^46+352x^47+681x^48+144x^49+336x^50+8x^51+19x^52+8x^54+1x^56+8x^58+1x^60+1x^64

The gray image is a linear code over GF(2) with n=368, k=12 and d=168.
This code was found by Heurico 1.16 in 74.4 seconds.