The generator matrix

1 0 0 0 0 1 1 1 1 1
0 1 0 0 0 1 0 X X X+1
0 0 1 0 0 1 X X+1 0 X
0 0 0 1 0 1 X+1 0 X X
0 0 0 0 1 X 1 X+1 1 X+1

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+40x^6+160x^7+130x^8+176x^10+320x^11+120x^12+40x^14+32x^15+5x^16

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 1.10 in 0 seconds.