The generator matrix

 1  0  1  1  1  6  1  1  1  1  4  2  1
 0  1  3  6  5  1  4  2  7  1  1  1  0

generates a code of length 13 over Z8 who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+6x^12+48x^13+6x^14+1x^16+2x^18

The gray image is a code over GF(2) with n=52, k=6 and d=24.
This code was found by Heurico 1.16 in 0.000287 seconds.