The generator matrix

 1  0  1  1  1  1  1
 0  1  3  0  0  0  0
 0  0  8  0  0  0  0
 0  0  0  8  0  0  0
 0  0  0  0  8  0  0
 0  0  0  0  0  8  0
 0  0  0  0  0  0  8

generates a code of length 7 over Z16 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+35x^2+161x^4+1211x^6+5376x^7+1211x^8+161x^10+35x^12+1x^14

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 0.0043 seconds.