The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^21+114x^22+174x^23+103x^24+42x^25+5x^26+10x^27+1x^42

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.