The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  2  1  1  1
 0 2X+2  0 2X+2  0 2X+2 2X  2  0 2X+2  0  0 2X+2 2X+2  2 2X 2X 2X  0  0
 0  0 2X  0  0  0 2X  0  0  0 2X  0 2X 2X 2X 2X 2X  0 2X  0
 0  0  0 2X  0  0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0 2X
 0  0  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0 2X 2X 2X  0
 0  0  0  0  0 2X  0 2X 2X 2X  0 2X  0 2X  0 2X 2X  0  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+39x^16+96x^18+64x^19+639x^20+64x^21+80x^22+24x^24+16x^26+1x^36

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 0.016 seconds.