The generator matrix

 1  0  0  1  1  1 3X  1  1  2  1 3X+2  1 3X+2  1  1  1  1  1  1
 0  1  0 2X+2  1 3X+1  1 3X  3  1  0  1 3X+1 2X  1  3 3X 3X+2 2X+3 2X
 0  0  1 3X+3  1 2X+2 2X+3 2X+3  X X+1 3X+2 3X+2 2X+1  1 3X+3 3X+1  3 X+1  1 2X
 0  0  0 2X 2X 2X  0  0  0 2X 2X 2X  0 2X  0 2X 2X  0 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+46x^16+406x^17+955x^18+1388x^19+2651x^20+1400x^21+874x^22+380x^23+61x^24+2x^25+19x^26+8x^27+1x^28

The gray image is a code over GF(2) with n=160, k=13 and d=64.
This code was found by Heurico 1.16 in 0.156 seconds.