The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+222x^17+501x^18+852x^19+1116x^20+718x^21+352x^22+242x^23+75x^24+12x^25+3x^26+2x^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 0.031 seconds.