The generator matrix

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

generates a code of length 9 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+60x^4+248x^6+750x^8+624x^10+332x^12+24x^14+9x^16

The gray image is a linear code over GF(2) with n=18, k=11 and d=4.
As d=4 is an upper bound for linear (18,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.16 in 0.00642 seconds.