The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  2  2
 0  2  0  6  0  6  0  6  4  0  0  4  6  6  6  2  6  6  6  6
 0  0  4  0  0  0  0  0  4  0  4  4  0  0  4  4  0  0  4  4
 0  0  0  4  0  0  0  4  0  0  4  4  0  4  4  0  0  4  4  0
 0  0  0  0  4  0  0  0  0  4  4  4  4  4  4  4  0  0  0  0
 0  0  0  0  0  4  0  4  0  4  4  0  4  0  4  0  0  0  4  4
 0  0  0  0  0  0  4  0  4  4  0  4  0  4  0  4  0  4  4  0

generates a code of length 20 over Z8 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+174x^16+672x^20+176x^24+1x^32

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 4.85 seconds.