The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  X  X  1  1  X  1
 0 X^2+2  0 X^2+2  2 X^2  2 X^2 X^2+2 X^2+2  0  2 X^2 X^2  0  2  0 X^2+2 X^2+2  0
 0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  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+6x^18+16x^19+82x^20+14x^21+6x^22+1x^24+2x^29

The gray image is a code over GF(2) with n=160, k=7 and d=72.
This code was found by Heurico 1.16 in 0 seconds.