The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1
 0  4  0  0  0  0  0  0  0  0  0  4  0
 0  0  4  0  0  0  0  0  0  0  0  4  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+55x^4+11x^6+330x^8+165x^10+462x^12+6144x^13+462x^14+165x^16+330x^18+11x^20+55x^22+1x^26

The gray image is a code over GF(2) with n=52, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0699 seconds.