The generator matrix

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

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+9x^10+24x^11+12x^12+6x^14+8x^15+3x^16+1x^18

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 0.000366 seconds.