The generator matrix

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

generates a code of length 53 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+92x^50+94x^52+6x^54+6x^56+26x^58+22x^60+2x^62+1x^64+2x^66+4x^68

The gray image is a linear code over GF(2) with n=106, k=8 and d=50.
As d=50 is an upper bound for linear (106,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 96.2 seconds.