The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  X  X  0 X^2  2 X^2+2
 0  X  0 X^2+X+2  2 X^2+X  0  X X^2 X^2+X+2 X^2+2 X+2 X^2+2  X  X X^2+2  X X^2+X X^2+2 X^2  2  X  X
 0  0 X^2+2  0  2 X^2+2 X^2+2 X^2 X^2 X^2  2 X^2 X^2 X^2+2 X^2  2 X^2 X^2 X^2 X^2  2  2  0
 0  0  0 X^2+2 X^2+2 X^2 X^2+2  2  0  0 X^2+2 X^2+2 X^2 X^2 X^2  2  0 X^2  2 X^2+2 X^2+2 X^2+2 X^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+300x^20+128x^21+464x^22+256x^23+548x^24+128x^25+144x^26+76x^28+3x^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 12.4 seconds.