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

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+32x^50+24x^51+92x^52+284x^53+28x^54+4x^55+8x^56+4x^57+28x^58+4x^59+2x^68+1x^72

The gray image is a linear code over GF(2) with n=424, k=9 and d=200.
This code was found by Heurico 1.16 in 0.125 seconds.