The generator matrix

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

generates a code of length 20 over Z8 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+34x^10+102x^12+162x^14+336x^16+804x^18+5260x^20+884x^22+356x^24+122x^26+78x^28+42x^30+11x^32

The gray image is a code over GF(2) with n=80, k=13 and d=20.
This code was found by Heurico 1.16 in 0.262 seconds.