The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+289x^20+416x^21+1038x^22+728x^23+940x^24+368x^25+252x^26+24x^27+25x^28+14x^30+1x^32

The gray image is a code over GF(2) with n=184, k=12 and d=80.
This code was found by Heurico 1.16 in 2.28 seconds.