The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+109x^20+24x^21+292x^22+328x^23+810x^24+1304x^25+1644x^26+2440x^27+2461x^28+2440x^29+1668x^30+1304x^31+859x^32+328x^33+228x^34+24x^35+99x^36+8x^38+10x^40+3x^44

The gray image is a code over GF(2) with n=112, k=14 and d=40.
This code was found by Heurico 1.16 in 3.14 seconds.