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

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+45x^22+80x^23+261x^24+80x^25+42x^26+2x^28+1x^46

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 -6.48e-008 seconds.