The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+188x^20+144x^22+64x^23+639x^24+576x^25+624x^26+1408x^27+904x^28+1408x^29+624x^30+576x^31+639x^32+64x^33+144x^34+188x^36+1x^56

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 49.1 seconds.