The generator matrix

 1  0  1  2  1  1  1
 0  1  1  4  0  0  0
 0  0  2  2  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+59x^2+144x^3+281x^4+1120x^5+5547x^6+18464x^7+5547x^8+1120x^9+281x^10+144x^11+59x^12+1x^14

The gray image is a code over GF(2) with n=56, k=15 and d=8.
This code was found by Heurico 1.16 in 0.0865 seconds.