The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  X  X
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+2  X X+2  0 X+2  0  2
 0  0  2  0  0  0  0  2  0  2  2  2  0  0  2  2  0  0  2  0
 0  0  0  2  0  0  2  2  0  2  0  2  0  2  2  0  2  0  0  2
 0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  0  0  2
 0  0  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  0  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+77x^16+262x^18+372x^20+230x^22+58x^24+18x^26+4x^28+2x^30

The gray image is a code over GF(2) with n=80, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0136 seconds.