The generator matrix

 1  0  1  2  2  1  1
 0  1  1  0  0  0  0
 0  0  2  2  0  0  0
 0  0  0  4 12  0  0
 0  0  0  0  8  0  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+224x^3+587x^4+1280x^5+6767x^6+14912x^7+6767x^8+1280x^9+587x^10+224x^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 0.0856 seconds.