The generator matrix

 1  0  0  1  1  1  2 X^2  1  X  1  1  X  1  1  1  1 X^2+X  1  2  1 X^2+X+2  1
 0  1  0 X^2 X^2+1  1  1  1  X  1 X^2+X+1 X^2+X  X  3 X^2+X+3 X^2+1 X+3  1 X^2+2  1 X^2+X+1  1 X^2+2
 0  0  1 X^2+X+1 X+1 X^2 X+3  X X^2+2 X^2+X+1  3 X^2+3  1 X^2+X X+2  1 X^2  X X^2+X+2  3 X^2+X+3  1  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+102x^20+768x^21+735x^22+1192x^23+435x^24+572x^25+188x^26+80x^27+6x^28+12x^29+5x^30

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 0.047 seconds.