The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1
 0 X^2+2  0 X^2  0 X^2  2 X^2  2  2 X^2+2 X^2+2  2  0 X^2+2 X^2  2 X^2 X^2+2  0
 0  0 X^2+2 X^2  2 X^2+2 X^2+2  2  2 X^2 X^2+2  2  0 X^2 X^2  0 X^2 X^2  0  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+18x^18+18x^19+183x^20+12x^21+21x^22+2x^23+1x^34

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 -6.48e-008 seconds.