The generator matrix

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

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+299x^16+744x^17+1802x^18+3308x^19+4008x^20+3464x^21+1804x^22+656x^23+232x^24+16x^25+42x^26+4x^27+4x^28

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.