The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^8+1x^16

The gray image is a linear code over GF(2) with n=32, k=6 and d=16.
As d=16 is an upper bound for linear (32,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.000389 seconds.