The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+161x^6+686x^8+1916x^10+2668x^12+1894x^14+729x^16+124x^18+12x^20+1x^22

The gray image is a linear code over GF(2) with n=24, k=13 and d=6.
As d=6 is an upper bound for linear (24,13,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 13.
This code was found by Heurico 1.16 in 37 seconds.