The generator matrix
1 0 0 1 1 1 0 1 1 X
0 1 0 1 0 1 1 0 0 0
0 0 1 1 1 0 1 0 0 0
0 0 0 X 0 0 0 0 0 X
0 0 0 0 X 0 0 0 0 X
0 0 0 0 0 X 0 0 0 X
0 0 0 0 0 0 X 0 0 X
0 0 0 0 0 0 0 X 0 X
0 0 0 0 0 0 0 0 X X
generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+69x^4+272x^6+1082x^8+1248x^10+1082x^12+272x^14+69x^16+1x^20
The gray image is a linear code over GF(2) with n=20, k=12 and d=4.
As d=4 is an upper bound for linear (20,12,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 12.
This code was found by Heurico 1.16 in 0.0297 seconds.