The generator matrix

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

generates a code of length 34 over Z2[X]/(X^2) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+177x^32+32x^36+40x^40+6x^48

The gray image is a linear code over GF(2) with n=68, k=8 and d=32.
As d=32 is an upper bound for linear (68,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 1.48 seconds.