The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+414x^16+768x^18+1744x^20+768x^22+384x^24+16x^28+1x^32

The gray image is a code over GF(2) with n=80, k=12 and d=32.
This code was found by Heurico 1.16 in 18.1 seconds.