The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+45x^16+148x^17+446x^18+1004x^19+826x^20+1024x^21+428x^22+112x^23+22x^24+12x^25+22x^26+4x^27+2x^28

The gray image is a code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.047 seconds.