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  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3 X^2  0 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^2 X^3  0 X^3 X^3+X^2 X^2 X^3 X^2 X^3  0 X^3+X^2 X^3+X^2 X^2  0 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3 X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^2 X^3  0 X^2 X^2 X^2 X^3 X^3  0  0 X^3+X^2 X^2 X^3  0 X^3+X^2
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^2 X^3 X^3+X^2  0 X^2 X^3 X^3  0 X^3+X^2 X^2 X^3+X^2  0 X^2 X^2 X^3 X^3+X^2  0 X^3  0  0 X^3+X^2 X^3  0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  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+60x^50+142x^52+640x^53+116x^54+56x^56+8x^58+1x^104

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 0.328 seconds.