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

generates a code of length 46 over Z2[X]/(X^4) who´s minimum homogenous weight is 41.

Homogenous weight enumerator: w(x)=1x^0+72x^41+274x^42+208x^43+611x^44+488x^45+812x^46+464x^47+597x^48+264x^49+246x^50+32x^51+4x^52+8x^53+10x^54+1x^60+2x^62+2x^64

The gray image is a linear code over GF(2) with n=368, k=12 and d=164.
This code was found by Heurico 1.16 in 3.73 seconds.