The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+180x^50+184x^52+120x^54+4x^56+20x^58+3x^64

The gray image is a linear code over GF(2) with n=416, k=9 and d=200.
This code was found by Heurico 1.16 in 0.375 seconds.