The generator matrix

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

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+166x^24+192x^28+143x^32+10x^40

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 1.16 in 1.34 seconds.