The generator matrix

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

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+120x^17+643x^18+816x^19+1074x^20+696x^21+530x^22+160x^23+45x^24+11x^26

The gray image is a code over GF(2) with n=160, k=12 and d=68.
This code was found by Heurico 1.16 in 0.047 seconds.