The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  X  1  1 X^3+X^2  1  1 X^3  1  1 X^2+X  1  1 X^2  1  1 X^3+X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  0  X X^3+X^2+X X^2  1  1  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  X X^2+X+1  1 X^3+X^2 X^3+1  1 X^3 X+1  1 X^2+X X^3+X^2+1  1 X^3+X X^3+X^2+X+1  1 X^2  1  1  0 X^3+X^2+X X^3+X^2 X^3+X X^2  0 X^2+X X^2  X X+1 X^3+X^2+1 X^3+X^2+X+1  1 X^3+X+1 X^3+X^2+1 X^3+X^2+X+1  1  1 X^3  1  1  1  X X^3  X X^3+X^2+X  X X^3
 0  0 X^2 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3  0 X^3 X^2  0 X^2  0 X^2  0 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^3 X^3+X^2  0 X^2 X^3+X^2  0 X^2 X^3 X^3 X^3 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  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+328x^50+120x^51+210x^52+48x^53+248x^54+24x^55+43x^56+1x^68+1x^76

The gray image is a linear code over GF(2) with n=416, k=10 and d=200.
This code was found by Heurico 1.16 in 8.58 seconds.