The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+8x^50+104x^52+8x^54+2x^56+4x^60+1x^64

The gray image is a linear code over GF(2) with n=208, k=7 and d=100.
This code was found by Heurico 1.16 in 0.0655 seconds.