The generator matrix

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

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+16x^18+64x^19+92x^20+64x^21+16x^22+2x^24+1x^32

The gray image is a code over GF(2) with n=160, k=8 and d=72.
This code was found by Heurico 1.16 in -1.01e-007 seconds.