The generator matrix

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

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+180x^16+698x^17+1858x^18+3274x^19+4314x^20+3484x^21+1728x^22+588x^23+217x^24+10x^25+22x^26+10x^27

The gray image is a code over GF(2) with n=160, k=14 and d=64.
This code was found by Heurico 1.16 in 0.625 seconds.