The generator matrix

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

generates a code of length 23 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+198x^21+202x^22+282x^23+165x^24+122x^25+14x^26+38x^27+2x^32

The gray image is a code over GF(2) with n=184, k=10 and d=84.
This code was found by Heurico 1.16 in 0.016 seconds.