The generator matrix

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

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+67x^42+228x^43+152x^44+520x^45+204x^46+440x^47+153x^48+176x^49+48x^50+36x^51+12x^52+8x^53+1x^58+2x^64

The gray image is a linear code over GF(2) with n=368, k=11 and d=168.
This code was found by Heurico 1.16 in 0.078 seconds.