The generator matrix

 1  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  0  4  0  0  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  0  0  4  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  0  0  4  0  0  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  0  0  4  0  0  4  0  0
 0  0  0  0  0  0  0  0  0  4  0  4  0  0
 0  0  0  0  0  0  0  0  0  0  4  4  0  0

generates a code of length 14 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+55x^4+341x^8+627x^12+6144x^14+627x^16+341x^20+55x^24+1x^28

The gray image is a code over GF(2) with n=56, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0698 seconds.