The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X
 0  X  0 X^2+X+2 X^2  X X^2+2 X^2+X  0 X^2+X+2  2 X^2+X+2 X^2+2 X^2+2  X X+2  2  2 X^2+X X^2+X+2
 0  0 X^2+2 X^2 X^2 X^2+2  0  0  2 X^2+2 X^2  2 X^2+2  2 X^2  2  2  0  0 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+76x^18+64x^19+229x^20+64x^21+76x^22+1x^24+1x^36

The gray image is a code over GF(2) with n=160, k=9 and d=72.
This code was found by Heurico 1.16 in 6.87e-008 seconds.