The generator matrix

 1  0  0  0  1  1  1  1  1  1  1  X
 0  1  0  0  1  0  0  1  1  0  0  0
 0  0  1  0  1  0  1  0  1  0  0  0
 0  0  0  1  1  1  0  0  1  0  0  0
 0  0  0  0  X  0  0  0  0  0  0  X
 0  0  0  0  0  X  0  0  0  0  0  X
 0  0  0  0  0  0  X  0  0  0  0  X
 0  0  0  0  0  0  0  X  0  0  0  X
 0  0  0  0  0  0  0  0  X  0  0  X
 0  0  0  0  0  0  0  0  0  X  0  X
 0  0  0  0  0  0  0  0  0  0  X  X

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+114x^4+512x^6+3247x^8+7168x^10+10684x^12+7168x^14+3247x^16+512x^18+114x^20+1x^24

The gray image is a linear code over GF(2) with n=24, k=15 and d=4.
As d=4 is an upper bound for linear (24,15,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 15.
This code was found by Heurico 1.16 in 1.61 seconds.