The generator matrix

 1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  1  1  1  1 X^2+2  X  2  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X+2 X^2+X+2  X X^2  X  2 X^2+2 X^2+X X+2  0 X^2+X  X  2 X^2 X^2+2
 0  0 X^2+2  0 X^2 X^2  2 X^2  0 X^2+2 X^2  2 X^2 X^2+2 X^2  0  0  2  2 X^2  2 X^2+2 X^2  0
 0  0  0  2  0  0  2  0  0  2  2  2  2  2  2  2  2  0  2  0  2  2  2  2
 0  0  0  0  2  0  0  2  2  0  0  2  2  2  0  2  2  2  0  2  2  2  0  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+87x^20+60x^21+249x^22+392x^23+499x^24+400x^25+242x^26+24x^27+42x^28+20x^29+21x^30+10x^32+1x^36

The gray image is a code over GF(2) with n=192, k=11 and d=80.
This code was found by Heurico 1.16 in 0.031 seconds.