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^2+2 X^2+X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  0  2 X^2+X X^2+X+2  2 X^2+X+2 X^2+2 X^2+X
 0  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  2
 0  0  0  2  2  2  2  0  2  0  0  2  0  0  2  2  0  2  0  2  2  2  2  2

generates a code of length 24 over Z4[X]/(X^3+2,2X) 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 code over GF(2) with n=192, k=9 and d=88.
This code was found by Heurico 1.16 in 0.015 seconds.