The generator matrix

 1  1  1  1  1  1  1  1  X  X  1  1  1  1  X  X X^2 X^2  0 X^3  X  X  1  1
 0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2  0 X^3

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+56x^24+4x^26+2x^28+1x^32

The gray image is a linear code over GF(2) with n=192, k=6 and d=96.
As d=96 is an upper bound for linear (192,6,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 6.
This code was found by Heurico 1.16 in 1.05e-007 seconds.