The generator matrix

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

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+498x^16+1300x^17+3510x^18+6952x^19+8103x^20+7184x^21+3550x^22+1176x^23+437x^24+28x^25+26x^26+1x^28+2x^30

The gray image is a code over GF(2) with n=160, k=15 and d=64.
This code was found by Heurico 1.16 in 3.22 seconds.