The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+132x^17+1202x^18+4162x^19+12287x^20+27646x^21+54174x^22+62492x^23+54631x^24+27984x^25+12294x^26+3786x^27+1045x^28+238x^29+42x^30+24x^31+4x^32

The gray image is a code over GF(2) with n=184, k=18 and d=68.
This code was found by Heurico 1.16 in 142 seconds.