The generator matrix

1 0 0 0 1 1 1 0 1 1 X 1 1 X 0 1 1 0 1 1 1 X 0 1 1 1 0 X
0 1 0 0 0 0 X 0 1 X+1 1 1 X 1 1 X+1 X X X X+1 X X 1 1 1 X+1 1 0
0 0 1 0 1 0 1 1 1 X X+1 X+1 X 1 0 X X+1 X 0 0 1 0 0 X X+1 X+1 0 X
0 0 0 1 1 X+1 0 X+1 X 0 X 1 X+1 X+1 0 X X 1 0 1 1 1 X X+1 X X+1 X+1 X
0 0 0 0 X X 0 X 0 0 0 0 0 0 X X X X X 0 X X 0 0 X X X X

generates a code of length 28 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+144x^24+64x^26+144x^28+36x^30+71x^32+24x^34+24x^36+4x^38

The gray image is a linear code over GF(2) with n=56, k=9 and d=24.
As d=24 is an upper bound for linear (56,9,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 9.
This code was found by Heurico 1.10 in 0.078 seconds.