The generator matrix

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

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+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 -1.16e-007 seconds.