The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+620x^20+864x^21+1808x^22+1744x^23+1698x^24+832x^25+536x^26+16x^27+64x^28+8x^30+1x^32

The gray image is a code over GF(2) with n=184, k=13 and d=80.
This code was found by Heurico 1.16 in 565 seconds.