The generator matrix

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

generates a code of length 24 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+106x^21+267x^22+480x^23+420x^24+422x^25+209x^26+96x^27+26x^28+12x^29+4x^30+4x^31+1x^36

The gray image is a code over GF(2) with n=192, k=11 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.