The generator matrix

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

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+122x^24+4x^28+1x^32

The gray image is a linear code over GF(2) with n=192, k=7 and d=96.
As d=96 is an upper bound for linear (192,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 3.81e-009 seconds.