The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  X  1  1  X  1  X  X  1  1  X  X  X  X  X  X  X  1  1  1  1  1  1  1  1  1  X  X  1  1  1  X  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2  0  0 X^3  0 X^3 X^3 X^3+X^2 X^2 X^2  0 X^2  0 X^2 X^2  0 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0 X^3 X^2  0 X^3+X^2 X^3+X^2  0
 0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0  0  0 X^3
 0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 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+8x^50+32x^51+174x^52+30x^53+7x^54+1x^56+2x^69+1x^70

The gray image is a linear code over GF(2) with n=416, k=8 and d=200.
This code was found by Heurico 1.16 in 0.094 seconds.