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.