The generator matrix

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

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+85x^4+52x^5+597x^6+444x^7+2034x^8+2452x^9+3532x^10+5244x^11+3874x^12+5244x^13+3566x^14+2452x^15+1997x^16+444x^17+620x^18+52x^19+73x^20+5x^22

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 1.11 in 0.0723 seconds.