The generator matrix

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

generates a code of length 10 over Z2[X]/(X^2) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+38x^5+97x^6+144x^7+228x^8+326x^9+367x^10+336x^11+244x^12+146x^13+79x^14+32x^15+7x^16+2x^17+1x^18

The gray image is a linear code over GF(2) with n=20, k=11 and d=5.
As d=5 is an upper bound for linear (20,11,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 11.
This code was found by Heurico 1.10 in 0.015 seconds.