The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+236x^17+437x^18+1068x^19+698x^20+1036x^21+358x^22+188x^23+37x^24+24x^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 0.859 seconds.