The generator matrix

 1  0  1  1  1 3X+2  1  1  1  1 2X X+2  1  1  1  1 X+2  1  1  1
 0  1 X+1 3X+2  3  1 3X+1  0 3X+2 2X+1  1  1 2X+3 3X+3 2X X+3  1  2 X+1  0
 0  0  2  0  0 2X  0  2 2X+2 2X+2 2X  2  2  2 2X+2  0 2X  0 2X  0
 0  0  0 2X+2 2X  2  2 2X+2  0  2 2X+2 2X+2 2X  2 2X 2X 2X 2X+2  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+55x^16+162x^17+465x^18+876x^19+1012x^20+862x^21+459x^22+128x^23+48x^24+14x^25+3x^26+4x^27+4x^28+2x^29+1x^30

The gray image is a code over GF(2) with n=160, k=12 and d=64.
This code was found by Heurico 1.16 in 0.047 seconds.