The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+141x^8+170x^10+389x^12+204x^14+106x^16+10x^18+3x^20

The gray image is a linear code over GF(2) with n=24, k=10 and d=8.
As d=8 is an upper bound for linear (24,10,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 10.
This code was found by Heurico 1.10 in 0 seconds.