The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+58x^24+4x^28+1x^32

The gray image is a linear code over GF(2) with n=96, k=6 and d=48.
As d=48 is an upper bound for linear (96,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.16 in 0.00397 seconds.