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

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+144x^50+64x^51+92x^52+64x^53+142x^54+2x^56+1x^64+2x^70

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 0.109 seconds.