The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+104x^20+128x^21+584x^22+768x^23+976x^24+768x^25+512x^26+128x^27+96x^28+24x^30+7x^32

The gray image is a code over GF(2) with n=192, k=12 and d=80.
This code was found by Heurico 1.16 in 0.079 seconds.