The generator matrix

 1  0  1  1  1  2 X^2+X  1  1 X^2+X+2  1  1  1  X  1  1  1 X^2  1  X
 0  1 X+1 X^2+X+2 X^2+1  1  1  2 X^2+X  1  3 X^2+X+1 X^2+3 X+2  3 X+1 X^2  1  X  1
 0  0 X^2 X^2+2  2 X^2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2+2 X^2+2 X^2+2 X^2+2 X^2+2 X^2 X^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+164x^18+272x^19+203x^20+224x^21+120x^22+16x^23+19x^24+4x^26+1x^28

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 0.016 seconds.