The generator matrix

 1  1  1  1  1  1  X  0
 0  X  0  X  0 X^2  X  X
 0  0  X  X  0  X X^2+X X^2
 0  0  0 X^2 X^2 X^2 X^2 X^2

generates a code of length 8 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+52x^6+32x^7+93x^8+32x^9+36x^10+10x^12

The gray image is a linear code over GF(2) with n=32, k=8 and d=12.
As d=13 is an upper bound for linear (32,8,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 8.
This code was found by Heurico 1.16 in 0.00047 seconds.