The generator matrix
1 0 0 0 0 0 0 0 1
0 1 0 0 0 0 0 0 1
0 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
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+72x^2+1548x^4+9240x^6+21942x^8+21816x^10+9324x^12+1512x^14+81x^16
The gray image is a linear code over GF(2) with n=18, k=16 and d=2.
As d=2 is an upper bound for linear (18,16,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 16.
This code was found by Heurico 1.11 in 0.00489 seconds.