The generator matrix

 1  0  0  1  1  1 X+2 X^2+X+2  2  1  1  1  1  0 X^2 X^2+X+2 X+2  1 X^2+2  1
 0  1  0 X^2 X^2+1  1  1  1 X^2+X+2 X^2+2 X^2+3 X^2 X^2+1  1  X X^2 X^2+X X+2  1  0
 0  0  1 X^2+X+1 X+1 X^2 X^2+1 X+3  1 X^2+X  X  1 X^2+1 X^2+X  1  1  1  3 X+3  2

generates a code of length 20 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+138x^17+609x^18+708x^19+1359x^20+542x^21+501x^22+160x^23+56x^24+20x^25+2x^26

The gray image is a code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 0.047 seconds.