The generator matrix

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

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+154x^16+64x^18+1612x^20+64x^22+148x^24+4x^28+1x^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 0.031 seconds.