The generator matrix

 1  0  0  1  1  1  2  0  1  1  1  2  0  1  1  1  1  2  1  2
 0  1  0  1  0  1  1  1  0  3  2  1  2  3  1  0  1  1  0  1
 0  0  1  1  1  0  1  2  0  0  3  2  1  2  1  3  3  2  2  1
 0  0  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  0  0  0
 0  0  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  2  0  2  2  2

generates a code of length 20 over Z4 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+105x^16+100x^18+124x^20+72x^22+86x^24+20x^26+4x^28

The gray image is a code over GF(2) with n=40, k=9 and d=16.
This code was found by Heurico 1.16 in 0.0128 seconds.