The generator matrix

1 0 0 0 0 0 1 1 1
0 1 0 0 0 0 0 1 1
0 0 1 0 0 0 0 1 X
0 0 0 1 0 0 1 0 1
0 0 0 0 1 0 1 0 X
0 0 0 0 0 1 1 X+1 1
0 0 0 0 0 0 X X 0

generates a code of length 9 over Z2[X]/(X^2) who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+24x^3+114x^4+272x^5+540x^6+1000x^7+1408x^8+1504x^9+1352x^10+1000x^11+582x^12+272x^13+92x^14+24x^15+7x^16

The gray image is a linear code over GF(2) with n=18, k=13 and d=3.
As d=3 is an upper bound for linear (18,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.10 in 0 seconds.