The generator matrix

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

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+30x^22+50x^23+78x^24+76x^25+16x^26+2x^27+1x^28+1x^30+1x^34

The gray image is a code over GF(2) with n=192, k=8 and d=88.
This code was found by Heurico 1.16 in -6.48e-008 seconds.