The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+50x^52+8x^54+3x^56+1x^60+1x^68

The gray image is a linear code over GF(2) with n=208, k=6 and d=104.
As d=104 is an upper bound for linear (208,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.0318 seconds.