The generator matrix

 1  0  1  1  1  0  1  1  1  1  4  6  0  1
 0  1  1  0  1  1  3  3  3  3  1  1  1  0
 0  0  2  0  0  0  6  0  2  2  0  4  0  0
 0  0  0  2  0  6  6  2  0  2  0  6  0  0
 0  0  0  0  2  0  6  2  2  0  2  6  0  0
 0  0  0  0  0  4  0  0  0  0  4  0  4  0
 0  0  0  0  0  0  4  0  0  4  4  4  0  0
 0  0  0  0  0  0  0  4  0  4  0  4  4  0
 0  0  0  0  0  0  0  0  4  4  4  4  4  4

generates a code of length 14 over Z8 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+33x^6+84x^7+182x^8+464x^9+1408x^10+2976x^11+6992x^12+12848x^13+15546x^14+12872x^15+6973x^16+2992x^17+1416x^18+448x^19+184x^20+80x^21+29x^22+4x^23+4x^24

The gray image is a code over GF(2) with n=56, k=16 and d=12.
This code was found by Heurico 1.16 in 3.4 seconds.