The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+18x^10+28x^12+13x^14+3x^16+1x^22

The gray image is a linear code over GF(2) with n=24, k=6 and d=10.
As d=10 is an upper bound for linear (24,6,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 6.
This code was found by Heurico 1.16 in 0.000467 seconds.