The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+91x^2+28x^3+1002x^4+728x^5+3094x^6+4004x^7+4004x^8+6864x^9+4004x^10+4004x^11+3094x^12+728x^13+1002x^14+28x^15+91x^16+1x^18

The gray image is a linear code over GF(2) with n=18, k=15 and d=2.
As d=2 is an upper bound for linear (18,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.11 in 0.00169 seconds.