The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+148x^17+206x^18+334x^19+702x^20+368x^21+146x^22+72x^23+32x^24+36x^25+2x^27+1x^32

The gray image is a code over GF(2) with n=160, k=11 and d=68.
This code was found by Heurico 1.16 in 0.031 seconds.