The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+246x^15+1595x^16+5340x^17+14248x^18+27112x^19+33448x^20+27858x^21+14584x^22+4854x^23+1352x^24+368x^25+48x^26+12x^27+4x^28+2x^29

The gray image is a code over GF(2) with n=160, k=17 and d=60.
This code was found by Heurico 1.16 in 32.3 seconds.