The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+70x^17+255x^18+464x^19+573x^20+366x^21+195x^22+76x^23+26x^24+16x^25+6x^26

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 0.015 seconds.