The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  1  1  1  1
 0  2  0  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2
 0  0  2  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0
 0  0  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  2  0  0
 0  0  0  0  2  0  0  2  0  2  0  2  0  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  2  2  0  0  2  0  0  2  2  2  0  2  0
 0  0  0  0  0  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+57x^16+32x^18+85x^20+32x^22+38x^24+10x^28+1x^36

The gray image is a code over GF(2) with n=40, k=8 and d=16.
This code was found by Heurico 1.16 in 0.00383 seconds.