The generator matrix

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

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+931x^16+2760x^17+7280x^18+12696x^19+17949x^20+13112x^21+7414x^22+2408x^23+838x^24+128x^25+16x^26+1x^28+2x^30

The gray image is a code over GF(2) with n=160, k=16 and d=64.
This code was found by Heurico 1.16 in 385 seconds.