The generator matrix

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

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+220x^19+877x^20+2034x^21+3146x^22+3770x^23+3414x^24+1886x^25+700x^26+264x^27+49x^28+14x^29+2x^30+2x^31+3x^32+2x^33

The gray image is a code over GF(2) with n=184, k=14 and d=76.
This code was found by Heurico 1.16 in 0.718 seconds.