The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+116x^19+285x^20+426x^21+754x^22+988x^23+740x^24+406x^25+228x^26+92x^27+37x^28+14x^29+2x^30+4x^31+1x^32+2x^33

The gray image is a code over GF(2) with n=184, k=12 and d=76.
This code was found by Heurico 1.16 in 0.094 seconds.