The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+12x^14+1x^16+2x^20

The gray image is a code over GF(2) with n=56, k=4 and d=28.
This code was found by Heurico 1.16 in 0.000546 seconds.