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

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+25x^50+80x^51+38x^52+736x^53+38x^54+80x^55+25x^56+1x^106

The gray image is a linear code over GF(2) with n=424, k=10 and d=200.
This code was found by Heurico 1.16 in 0.172 seconds.