The generator matrix
1 0 0 0 1 0 1 1 X 0
0 1 0 0 0 1 0 1 X 1
0 0 1 0 0 1 1 1 0 X
0 0 0 1 1 0 X+1 X 1 X
0 0 0 0 X 0 X 0 0 X
0 0 0 0 0 X X 0 X X
generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+97x^6+232x^8+351x^10+268x^12+63x^14+11x^16+1x^18
The gray image is a linear code over GF(2) with n=20, k=10 and d=6.
As d=6 is an upper bound for linear (20,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.16 in 0.00839 seconds.