The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  1
 0  1  0  0  0  1  3  1  1  2  3  2  0
 0  0  1  0  1  0  3  3  2  1  7  6  0
 0  0  0  1  1  3  0  1  2  4  3  7  0
 0  0  0  0  2  2  2  4  6  0  0  4  6

generates a code of length 13 over Z8 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+69x^8+382x^9+936x^10+1720x^11+3380x^12+3380x^13+3317x^14+1928x^15+896x^16+254x^17+98x^18+16x^19+6x^20+1x^22

The gray image is a code over GF(2) with n=52, k=14 and d=16.
This code was found by Heurico 1.11 in 0.297 seconds.