The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+89x^6+32x^7+597x^8+288x^9+2312x^10+1504x^11+8476x^12+10464x^13+18034x^14+10464x^15+8399x^16+1504x^17+2400x^18+288x^19+564x^20+32x^21+77x^22+11x^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 3.54 seconds.