The generator matrix

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

generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+4x^10+22x^12+4x^14+1x^24

The gray image is a linear code over GF(2) with n=24, k=5 and d=10.
This code was found by Heurico 1.16 in 0.000296 seconds.