The generator matrix

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

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+294x^16+224x^18+1024x^20+224x^22+264x^24+16x^28+1x^32

The gray image is a code over GF(2) with n=80, k=11 and d=32.
This code was found by Heurico 1.16 in 20 seconds.