The generator matrix

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

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+117x^20+192x^21+626x^22+192x^23+621x^24+192x^25+88x^26+11x^28+6x^30+2x^32

The gray image is a code over GF(2) with n=184, k=11 and d=80.
This code was found by Heurico 1.16 in 0.015 seconds.