The generator matrix

 1  0  1  1  1  X  1  1  0  1  1  1 X+2  1  1 X^2+2  1  1  1  1  1  X  1
 0  1  1 X^2 X+1  1  X X^2+1  1 X^2+X X^2+3 X^2  1 X+3 X+1  0 X^2+X+2  X  3  2 X^2+2  1  2
 0  0  X X+2  2 X+2 X+2 X^2+X+2 X^2+X+2  0 X^2+2 X^2+X  0 X^2 X^2+X+2  X X^2 X^2+X+2  2 X^2 X^2 X^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+75x^20+314x^21+394x^22+592x^23+300x^24+246x^25+72x^26+28x^27+16x^28+4x^29+5x^30+1x^34

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 0.016 seconds.