The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+251x^20+144x^21+1124x^22+1048x^23+3936x^24+3688x^25+8898x^26+7384x^27+12445x^28+7432x^29+9034x^30+3720x^31+4002x^32+1016x^33+1014x^34+136x^35+215x^36+8x^37+26x^38+12x^40+1x^44+1x^48

The gray image is a code over GF(2) with n=112, k=16 and d=40.
This code was found by Heurico 1.16 in 80.9 seconds.