The generator matrix

 1  1  1  1  1  1  1  1  1  0  1  1  1 X^2+2 X^2+2  1  1  1  1  X  1  X X^2  1
 0  X  0  X  2 X+2  0  X X^2  X X^2+X+2 X^2 X^2+X+2  X X^2+2 X^2+2 X^2 X^2+X X^2+X+2 X^2+2  X X^2+X+2  X  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2 X^2+X  X  0 X^2+X  X X^2+X  0 X^2  X X+2 X^2+X+2 X^2+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+56x^21+142x^22+206x^23+274x^24+160x^25+109x^26+42x^27+12x^28+12x^29+5x^30+4x^31+1x^36

The gray image is a code over GF(2) with n=192, k=10 and d=84.
This code was found by Heurico 1.16 in 3.81e-009 seconds.