The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+79x^16+268x^17+317x^18+852x^19+1134x^20+788x^21+311x^22+236x^23+64x^24+32x^25+11x^26+2x^28+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 0.062 seconds.