The generator matrix

 1  1  1  1  1  1  1  1  1  0  1  1  1 X^2+2 X^2+2  1  1  1  1  X  1  1  1
 0  X  0  X  2 X+2  0  X X^2  X X^2+X+2 X^2 X^2+X+2  X X^2+2 X^2+2 X^2 X^2+X X^2+X+2 X^2+2  X X^2+X  0
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2  2 X^2+X  X  0 X^2+X  X X^2+X  0 X^2  X X+2 X^2+X+2 X^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+52x^20+96x^21+249x^22+276x^23+227x^24+56x^25+26x^26+20x^27+16x^28+4x^30+1x^38

The gray image is a code over GF(2) with n=184, k=10 and d=80.
This code was found by Heurico 1.16 in 0.015 seconds.