The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  0  1  1  X  1  1  1  1  1
 0  X  0 X+2  2 3X+2 2X+2  X  0 2X X+2  X 2X+2 2X+2 3X+2  X X+2 3X  0 2X+2
 0  0 2X+2  0  2  2 2X  2  0  2  0 2X  2  0 2X+2 2X+2  2 2X 2X 2X
 0  0  0 2X 2X  0 2X 2X 2X 2X  0  0  0  0 2X  0 2X 2X 2X  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+48x^17+84x^18+220x^19+341x^20+196x^21+84x^22+36x^23+1x^24+12x^25+1x^36

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 0.016 seconds.