The generator matrix

 1  0  1  1  1  2  1
 0  1 11  0  0  0  0
 0  0 12  0  0 12  0
 0  0  0 12  0 12  0
 0  0  0  0 12 12  0
 0  0  0  0  0  8  0

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

Homogenous weight enumerator: w(x)=1x^0+69x^2+164x^3+619x^4+1264x^5+5455x^6+17624x^7+5455x^8+1264x^9+619x^10+164x^11+69x^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 0.0761 seconds.