The generator matrix

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

generates a code of length 28 over Z8 who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+174x^16+78x^19+264x^20+112x^21+252x^22+914x^23+772x^24+1376x^25+408x^26+3884x^27+208x^28+3072x^29+788x^30+1988x^31+457x^32+544x^33+336x^34+294x^35+168x^36+16x^37+228x^38+10x^39+4x^40+24x^42+12x^46

The gray image is a code over GF(2) with n=112, k=14 and d=32.
This code was found by Heurico 1.16 in 2.87 seconds.