The generator matrix

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

generates a code of length 14 over Z8 who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+32x^7+130x^8+416x^9+1328x^10+3680x^11+7805x^12+12256x^13+14240x^14+12256x^15+7805x^16+3680x^17+1328x^18+416x^19+130x^20+32x^21+1x^28

The gray image is a code over GF(2) with n=56, k=16 and d=14.
This code was found by Heurico 1.16 in 32.5 seconds.