The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  X  1  X  X  1  2  1  0  X
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X  0 X^2+X X^2+2  2 X^2+2  X X^2+X+2 X^2+X+2 X^2+X  X X^2  X X^2+2  0 X+2
 0  0 X^2+2  0 X^2 X^2  2 X^2  0  2  0 X^2 X^2  2 X^2 X^2+2  2 X^2+2 X^2+2 X^2  2 X^2  2
 0  0  0  2  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  0  2  2
 0  0  0  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  0  0  0  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+291x^20+64x^21+584x^22+128x^23+707x^24+64x^25+152x^26+49x^28+8x^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 3.22 seconds.