The generator matrix

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

generates a code of length 24 over Z2[X]/(X^4) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+48x^22+414x^24+48x^26+1x^48

The gray image is a linear code over GF(2) with n=192, k=9 and d=88.
This code was found by Heurico 1.16 in 0.031 seconds.