The generator matrix

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

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+58x^17+284x^18+416x^19+637x^20+314x^21+234x^22+56x^23+26x^24+16x^25+1x^26+4x^27+1x^30

The gray image is a code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.015 seconds.