The generator matrix

 1  0  0  1  1  1  6  1  1  1  1  2  1  1  2  4  1  4  1  1
 0  1  0  1  0  7  1  7  4  2  3  1  2  6  1  1  4  0  5  0
 0  0  1  1  1  0  1  1  0  5  4  3  7  3  2  6  4  2  7  0
 0  0  0  2  0  0  0  0  6  6  2  4  4  6  2  2  4  4  2  0
 0  0  0  0  2  6  6  4  4  6  2  2  0  0  6  2  6  6  4  0

generates a code of length 20 over Z8 who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+42x^14+184x^15+384x^16+702x^17+867x^18+1102x^19+1513x^20+1276x^21+901x^22+676x^23+303x^24+134x^25+77x^26+22x^27+7x^28+1x^30

The gray image is a code over GF(2) with n=80, k=13 and d=28.
This code was found by Heurico 1.16 in 0.404 seconds.