The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  0  0  0  0  1
 0  1  1  0 X+1  1  0 X+1  1  0  1  1  X X+1  1  X X+1  1  X  1  1  X  1  1  0  0  0  0  X  X  X  X X+1 X+1 X+1 X+1  1  1  1  1  0  0  0  X  X  X  0  X  1  1  1  1  0
 0  0  X  0  X  0  X  0  X  X  0  X  X  0  X  0  X  0  X  X  X  0  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0
 0  0  0  X  X  X  X  0  0  0  X  X  0  X  0  X  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  0  0  X  X  0  0

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+14x^52+28x^53+14x^54+1x^56+2x^57+1x^58+2x^65+1x^66

The gray image is a linear code over GF(2) with n=106, k=6 and d=52.
As d=52 is an upper bound for linear (106,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0193 seconds.