The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+166x^20+670x^21+741x^22+1156x^23+570x^24+482x^25+201x^26+88x^27+15x^28+4x^29+2x^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 0.062 seconds.