The generator matrix

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

generates a code of length 20 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+18x^16+34x^17+84x^18+44x^19+702x^20+16x^21+66x^22+20x^23+15x^24+14x^25+9x^26+1x^34

The gray image is a code over GF(2) with n=160, k=10 and d=64.
This code was found by Heurico 1.16 in -1.01e-007 seconds.