The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+224x^15+908x^16+3156x^17+6957x^18+13252x^19+16392x^20+13624x^21+6770x^22+3096x^23+905x^24+180x^25+65x^26+4x^27+2x^28

The gray image is a code over GF(2) with n=160, k=16 and d=60.
This code was found by Heurico 1.16 in 7.67 seconds.