The generator matrix
1 0 1 1 1 X 1 1 1 1 0 X 1 1 1 1 X X 0 0 X
0 1 X+1 X 1 1 0 X X+1 1 1 1 0 X X+1 1 0 X X 1 1
generates a code of length 21 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.
Homogenous weight enumerator: w(x)=1x^0+12x^22+3x^24
The gray image is a linear code over GF(2) with n=42, k=4 and d=22.
As d=22 is an upper bound for linear (42,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.00101 seconds.