The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^16+416x^17+945x^18+1518x^19+2470x^20+1504x^21+818x^22+380x^23+77x^24+16x^25+13x^26+6x^27

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 0.14 seconds.