The generator matrix

 1  0  1  1 X^2+X  1  1  1  0  1  1  X  1  1 X+2  1  X X+2  X  1
 0  1  1 X^2+X  1 X+3 X^2+3 X^2  1  X X^2+X+3  1 X^2  1  1 X^2+3 X^2+X  1 X^2  2
 0  0  X  0  2 X^2 X^2+2 X+2 X^2+X+2  X X^2+X+2 X+2 X^2+X+2 X^2+X X^2+X X+2 X^2+X+2  0 X+2 X+2
 0  0  0  2  2  0  2  0  2  2  2  0  0  0  2  2  0  0  2  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+192x^17+677x^18+564x^19+1258x^20+636x^21+566x^22+116x^23+53x^24+20x^25+5x^26+8x^27

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 0.078 seconds.