The generator matrix

 1  0  0  1  1  1  X  1 X^2+X  1  X  1  1 X^2  1  X  1  0  1 X^2+X X^2  1  0 X^2+X
 0  1  0 X^2 X^2+1  1  1  0  1  X  1  1 X+1  X X^2  0 X^2+1  1  X  1  1 X^2+X+1  1 X^2+X
 0  0  1 X^2+X+1 X+1 X^2 X^2+1  X  0 X^2+1 X+1  1 X^2  1 X^2+1  1 X^2+X  X X^2+X+1 X^2 X+1  X X^2+1  1

generates a code of length 24 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+212x^22+146x^24+104x^26+28x^28+20x^30+1x^32

The gray image is a linear code over GF(2) with n=96, k=9 and d=44.
As d=44 is an upper bound for linear (96,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by Heurico 1.16 in 0.0171 seconds.