The generator matrix

 1  0  0  1  1  1  X  1  1  X  1  1  0  X  1  1  X  0  1  1  X  0  1  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0  X  X  X  X  0  0  1
 0  1  0  X  1 X+1  1  X  0  0  1 X+1  1  1 X+1  1  1  1 X+1  1  1  1  X  0  X  X  0  X  0  0  X  X  X  X  0  0  1  1 X+1 X+1 X+1 X+1  1  1  1  1  1  1  1  1  1  1  0
 0  0  1  1 X+1  X  1 X+1  X  1  1  0  X X+1 X+1  X  X X+1  1  0  0  1  X X+1  1  0  1  1  0  X  X  0  1 X+1 X+1  1  1 X+1 X+1  1  0  X  X  0  0  X  X  0  1 X+1 X+1  1  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+12x^52+32x^53+12x^54+2x^56+2x^58+1x^64+2x^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 0.0181 seconds.