The generator matrix
1 0 1 X 1 1 1 1 1 1 1 1
0 1 X 1 X+1 1 0 X X+1 1 0 X
generates a code of length 12 over Z2[X]/(X^2) who´s minimum homogenous weight is 12.
Homogenous weight enumerator: w(x)=1x^0+13x^12+1x^16+1x^20
The gray image is a linear code over GF(2) with n=24, k=4 and d=12.
As d=12 is an upper bound for linear (24,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.000231 seconds.