The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X^2+X X+2  0 X^2+2 X+2 X^2+2 X^2  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  1  1  1  1  X  X  0 X^2+2
 0  0  2  0  2  0  0  2  0  0  2  0  2  0  0  2  2  2  0  2
 0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  2  0  2  2

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+201x^18+192x^19+251x^20+192x^21+176x^22+3x^24+6x^26+1x^28+1x^34

The gray image is a code over GF(2) with n=160, k=10 and d=72.
This code was found by Heurico 1.16 in 1.08 seconds.