The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+126x^18+1148x^19+3250x^20+7490x^21+12833x^22+15688x^23+13067x^24+7654x^25+3016x^26+1012x^27+208x^28+22x^29+9x^30+8x^31+2x^32+2x^33

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 seconds.