The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^20+34x^21+124x^22+170x^23+400x^24+646x^25+925x^26+1234x^27+1146x^28+1170x^29+864x^30+606x^31+419x^32+194x^33+122x^34+38x^35+33x^36+4x^37+12x^38+4x^40+1x^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 0.792 seconds.