The generator matrix
1 0 1 1 1 1 1 1 1
0 1 1 0 0 0 0 0 0
0 0 X 0 0 0 0 0 0
0 0 0 X 0 0 0 0 0
0 0 0 0 X 0 0 0 0
0 0 0 0 0 X 0 0 0
0 0 0 0 0 0 X 0 0
0 0 0 0 0 0 0 X 0
0 0 0 0 0 0 0 0 X
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+13x^2+64x^4+168x^6+778x^8+778x^10+168x^12+64x^14+13x^16+1x^18
The gray image is a linear code over GF(2) with n=18, k=11 and d=2.
This code was found by Heurico 1.16 in 0.0058 seconds.