The generator matrix

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

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+100x^50+43x^52+62x^54+13x^56+18x^58+5x^60+4x^62+2x^64+6x^66+2x^70

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 51.6 seconds.