The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+84x^14+648x^15+3082x^16+10154x^17+28875x^18+52712x^19+70008x^20+54268x^21+29074x^22+9504x^23+2839x^24+682x^25+175x^26+32x^27+6x^28

The gray image is a code over GF(2) with n=160, k=18 and d=56.
This code was found by Heurico 1.16 in 107 seconds.