The generator matrix

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

generates a code of length 13 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+79x^4+179x^6+858x^8+512x^9+1173x^10+5120x^11+1806x^12+13312x^13+1806x^14+5120x^15+1173x^16+512x^17+858x^18+179x^20+79x^22+1x^26

The gray image is a code over GF(2) with n=52, k=15 and d=8.
This code was found by Heurico 1.16 in 0.751 seconds.