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  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
 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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+12x^50+32x^51+12x^52+2x^54+2x^56+2x^62+1x^64

The gray image is a linear code over GF(2) with n=102, k=6 and d=50.
As d=50 is an upper bound for linear (102,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.0158 seconds.