The generator matrix

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

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+252x^24+3x^32

The gray image is a linear code over GF(2) with n=192, k=8 and d=96.
As d=96 is an upper bound for linear (192,8,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 8.
This code was found by Heurico 1.16 in 1.05e-007 seconds.