The generator matrix

 1  0  1  1  1  0  1  1  1  1  X  1
 0  1  1  0  1  1  0  X  0  0  0  X
 0  0  X  0  0  0  X  X  0  0  X  X
 0  0  0  X  0  0  X  0  X  X  0  X
 0  0  0  0  X  0  X  X  X  X  X  X
 0  0  0  0  0  X  X  X  0  X  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+22x^8+8x^9+32x^10+72x^11+24x^12+24x^13+24x^14+24x^15+17x^16+8x^18

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 -3.81e-008 seconds.