The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1 X^2  1  1  1  1  1  X  1  1  1 X^2  1  1  1 X^2 X^2  1 X^3+X^2  X  X  X  1
 0  X  0  X  0 X^3 X^2+X  X X^2 X^2+X X^2 X^3+X^2+X X^2 X^3+X^2 X^3+X X^3+X^2+X X^3+X X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X X^2+X X^3 X^2 X^2 X^2 X^3+X^2+X X^3 X^2 X^3+X^2+X X^3+X X^3  X  X X^3+X^2 X^3 X^2+X  0  X X^3+X^2  X X^3  X X^3+X^2  0
 0  0  X  X X^3+X^2 X^3+X^2+X X^2+X X^2 X^3+X^2 X^3  0 X^3+X^2  X X^2+X X^2+X  X X^3+X  X  0 X^3+X^2 X^3+X X^3+X^2+X X^2 X^3+X^2+X  X X^3+X X^3+X^2 X^3+X^2+X X^3 X^2 X^3+X^2  0  X X^2 X^2 X^3+X  X X^3  X X^3+X  0 X^3+X^2+X X^3+X^2+X X^3+X X^3+X  0
 0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3
 0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 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+104x^41+178x^42+412x^43+397x^44+684x^45+714x^46+650x^47+294x^48+306x^49+166x^50+88x^51+27x^52+56x^53+14x^54+2x^55+2x^57+1x^72

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 0.265 seconds.