The generator matrix

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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+258x^43+316x^44+380x^45+317x^46+274x^47+221x^48+184x^49+17x^50+38x^51+21x^52+12x^53+6x^55+1x^58+1x^60+1x^62

The gray image is a linear code over GF(2) with n=368, k=11 and d=172.
This code was found by Heurico 1.16 in 31.3 seconds.