The generator matrix

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

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+86x^8+168x^9+76x^10+144x^12+304x^13+168x^14+25x^16+40x^17+12x^18

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 1.16 in 0.014 seconds.