The generator matrix

 1  0  0  1  1
 0  1  0  1  X
 0  0  1  X  1

generates a code of length 5 over Z2[X]/(X^3) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+48x^3+98x^4+224x^5+88x^6+48x^7+5x^8

The gray image is a linear code over GF(2) with n=20, k=9 and d=6.
As d=7 is an upper bound for linear (20,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.11 in 1.05e-007 seconds.