The generator matrix

 1  1  1  1  X  0  X X^2  1
 0  X X^2 X^2+X X^2+X  X  X  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+2x^8+24x^9+3x^10+1x^12+1x^14

The gray image is a linear code over GF(2) with n=36, k=5 and d=16.
As d=17 is an upper bound for linear (36,5,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 5.
This code was found by Heurico 1.16 in 0.000183 seconds.