The generator matrix

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

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+81x^8+24x^10+22x^12

The gray image is a linear code over GF(2) with n=36, k=7 and d=16.
As d=16 is an upper bound for linear (36,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.0048 seconds.