The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1
0 X 0 0 0 0 0 0 0 X 0 0
0 0 X 0 0 0 0 0 0 X 0 0
0 0 0 X 0 0 0 0 0 X 0 0
0 0 0 0 X 0 0 0 0 X 0 0
0 0 0 0 0 X 0 0 0 X 0 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+36x^4+135x^8+680x^12+135x^16+36x^20+1x^24
The gray image is a linear code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00456 seconds.