The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1
 0 X^2+2  0 X^2  0  2 X^2+2 X^2+2  0 X^2 X^2  2  2 X^2  0 X^2 X^2+2 X^2+2  2  0  0  2  0
 0  0 X^2+2 X^2  0 X^2 X^2  2  2 X^2  2  2 X^2 X^2+2 X^2+2  0  0  2 X^2+2 X^2+2  2  2  0
 0  0  0  2  2  2  0  2  2  0  0  0  0  2  2  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+28x^20+132x^22+192x^23+133x^24+20x^26+5x^28+1x^44

The gray image is a code over GF(2) with n=184, k=9 and d=80.
This code was found by Heurico 1.16 in 3.62e-008 seconds.