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.