The generator matrix

 1  0  0  0  0  1  1  1  0  X  1  1
 0  1  0  0  0  0  1  1  1  0  0  0
 0  0  1  0  0  1  1  0  1  0  0  0
 0  0  0  1  0  1  0  1  1  0  0  0
 0  0  0  0  1  1  0  0  0  0  X  0
 0  0  0  0  0  X  0  0  0  X  X  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  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+76x^4+427x^6+1654x^8+3644x^10+4780x^12+3658x^14+1617x^16+460x^18+64x^20+3x^22

The gray image is a linear code over GF(2) with n=24, k=14 and d=4.
This code was found by Heurico 1.16 in 0.935 seconds.