The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+3x^20+8x^21+3x^22+1x^26

The gray image is a code over GF(2) with n=40, k=4 and d=20.
This code was found by Heurico 1.16 in 0.000979 seconds.