The generator matrix

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

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+63x^4+44x^5+252x^6+252x^7+447x^8+728x^9+526x^10+728x^11+433x^12+252x^13+272x^14+44x^15+48x^16+6x^18

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 1.10 in 0.016 seconds.