The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  1
 0  1  0  0  0  0  0  0  1  0  1  X
 0  0  1  0  0  0  0  0  1  0  X  0
 0  0  0  1  0  0  0  0  1  1 X+1  0
 0  0  0  0  1  0  0  0  1  X  0  0
 0  0  0  0  0  1  0  0  1  X  X  0
 0  0  0  0  0  0  1  0  1 X+1  1  0
 0  0  0  0  0  0  0  1  1 X+1 X+1  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+121x^4+82x^5+738x^6+936x^7+3158x^8+4888x^9+7428x^10+10488x^11+9870x^12+10460x^13+7448x^14+4888x^15+3129x^16+952x^17+764x^18+72x^19+105x^20+2x^21+6x^22

The gray image is a linear code over GF(2) with n=24, k=16 and d=4.
As d=4 is an upper bound for linear (24,16,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 16.
This code was found by Heurico 1.11 in 0.544 seconds.