The generator matrix
1 0 X X 1 1 1 X 1 0 1 1 1 X 1 0 1 X 1 1 X 0 1 0 1 X 1 1
0 1 X X X+1 1 X 1 0 1 X+1 1 X 1 0 1 X 1 X+1 1 0 X 0 1 X 0 X+1 1
generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+8x^29+4x^30+3x^32
The gray image is a linear code over GF(2) with n=56, k=4 and d=29.
As d=29 is an upper bound for linear (56,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.132 seconds.