The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+78x^4+715x^8+3764x^12+8192x^13+2048x^14+1287x^16+286x^20+13x^24

The gray image is a code over GF(2) with n=52, k=14 and d=8.
This code was found by Heurico 1.16 in 0.323 seconds.