The generator matrix

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

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+45x^8+66x^10+37x^12+60x^14+42x^16+2x^18+3x^20

The gray image is a linear code over GF(2) with n=24, k=8 and d=8.
As d=8 is an upper bound for linear (24,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.000956 seconds.