The generator matrix

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

generates a code of length 23 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+166x^18+1170x^19+3133x^20+7328x^21+13060x^22+15736x^23+13231x^24+7440x^25+2918x^26+1058x^27+243x^28+32x^29+16x^30+4x^31

The gray image is a code over GF(2) with n=184, k=16 and d=72.
This code was found by Heurico 1.16 in 10.2 seconds.