The generator matrix

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

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+74x^18+582x^19+1737x^20+3656x^21+6891x^22+6968x^23+6755x^24+3778x^25+1702x^26+478x^27+107x^28+20x^29+11x^30+4x^31+2x^33+2x^34

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 2.58 seconds.