The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+21x^16+10x^18+32x^19+32x^21+15x^22+10x^24+6x^26+1x^38

The gray image is a code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.00156 seconds.