The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1  4  1  1  1  6  4  6  1  6  1  0  1  2  1
 0  1  1  0  3  1  3  0  1  5  1  5  2  4  1  1  6  3  1  2  1  1  1  0  0  4  2  0
 0  0  2  0  0  0  0  2  2  6  2  4  2  2  2  0  2  6  4  2  2  0  0  4  4  6  2  2
 0  0  0  2  0  6  6  2  6  6  0  4  0  4  4  6  2  2  4  0  2  2  4  0  2  0  4  2
 0  0  0  0  4  0  0  0  0  0  0  0  4  4  4  0  0  4  0  0  4  4  4  4  0  0  4  0
 0  0  0  0  0  4  0  0  0  4  4  4  4  0  4  4  0  4  0  4  4  4  0  4  4  0  0  0
 0  0  0  0  0  0  4  0  4  0  4  4  0  0  0  4  4  4  4  4  0  4  0  4  4  4  4  0
 0  0  0  0  0  0  0  4  0  0  0  0  0  0  0  0  4  4  4  4  4  4  4  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+61x^20+92x^21+291x^22+372x^23+955x^24+976x^25+2260x^26+1596x^27+3076x^28+1680x^29+2306x^30+1004x^31+977x^32+320x^33+244x^34+100x^35+45x^36+4x^37+19x^38+3x^40+2x^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 3.19 seconds.