The generator matrix

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

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+24x^17+166x^18+174x^19+375x^20+112x^21+96x^22+38x^23+24x^24+4x^25+9x^26+1x^30

The gray image is a code over GF(2) with n=160, k=10 and d=68.
This code was found by Heurico 1.16 in 0.015 seconds.