The generator matrix

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

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+138x^18+692x^19+1839x^20+3832x^21+6173x^22+7246x^23+6517x^24+3830x^25+1676x^26+588x^27+161x^28+64x^29+5x^30+2x^31+2x^32+2x^33

The gray image is a code over GF(2) with n=184, k=15 and d=72.
This code was found by Heurico 1.16 in 2.83 seconds.