The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  X
 0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0 X^2+2  0 X^2+2  0 X^2+2  2 X^2  0  2  2 X^2+2 X^2 X^2+2 X^2+2
 0  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  0  0  0  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  0  0  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  2  0  2  2  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+35x^20+32x^21+32x^22+320x^23+30x^24+32x^25+16x^26+13x^28+1x^40

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 0.016 seconds.