The generator matrix

1 1 1 1 1 1 1 2 2 2 2 2 2 2
0 2 0 2 6 4 4 4 2 2 6 6 0 0
0 0 4 4 4 0 4 4 0 4 0 4 4 0

generates a code of length 14 over Z8 who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+14x^13+40x^14+7x^16+2x^21

The gray image is a code over GF(2) with n=56, k=6 and d=26.
This code was found by an older version of Heurico in 0 seconds.