The generator matrix

 1  1  2  1  1  1  1
 0  2  2  0  0  0  0
 0  0  4  0  0  8  0
 0  0  0 12  0  8  0
 0  0  0  0 12  8  0

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

Homogenous weight enumerator: w(x)=1x^0+36x^2+42x^3+142x^4+216x^5+1357x^6+4604x^7+1357x^8+216x^9+142x^10+42x^11+36x^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 0.00955 seconds.