The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+52x^21+233x^22+80x^23+30x^24+36x^25+70x^26+8x^27+1x^28+1x^34

The gray image is a code over GF(2) with n=184, k=9 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.