The generator matrix

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

generates a code of length 28 over Z8 who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+78x^20+76x^21+162x^22+300x^23+379x^24+488x^25+810x^26+1192x^27+1239x^28+1114x^29+819x^30+652x^31+368x^32+166x^33+167x^34+96x^35+47x^36+10x^37+23x^38+2x^41+3x^42

The gray image is a code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 1.22 seconds.