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^2  X
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X  0 X^3 X^2+X X^3+X^2+X X^3 X^3+X^2+X X^3+X^2 X^2+X
 0  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3
 0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 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+76x^22+80x^23+201x^24+80x^25+68x^26+5x^28+1x^44

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 seconds.