The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+23x^8+16x^9+22x^10+2x^14

The gray image is a linear code over GF(2) with n=36, k=6 and d=16.
As d=16 is an upper bound for linear (36,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.000162 seconds.