The generator matrix

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

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+188x^4+1128x^6+4006x^8+5752x^10+3964x^12+1176x^14+161x^16+8x^18

The gray image is a linear code over GF(2) with n=20, k=14 and d=4.
As d=4 is an upper bound for linear (20,14,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 14.
This code was found by Heurico 1.10 in 0.032 seconds.