The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+62x^16+48x^17+192x^18+464x^19+518x^20+464x^21+192x^22+48x^23+54x^24+2x^28+3x^32

The gray image is a code over GF(2) with n=160, k=11 and d=64.
This code was found by Heurico 1.16 in 0.016 seconds.