The generator matrix

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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+248x^52+4x^56+3x^64

The gray image is a linear code over GF(2) with n=416, k=8 and d=208.
This code was found by Heurico 1.16 in 2.72 seconds.