The generator matrix
1 0 1 1 1 0 1 1 X
0 1 1 0 1 1 0 0 0
0 0 X 0 0 0 0 0 X
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+44x^4+104x^6+398x^8+272x^10+188x^12+8x^14+9x^16
The gray image is a linear code over GF(2) with n=18, k=10 and d=4.
As d=4 is an upper bound for linear (18,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.00312 seconds.