The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^2+202x^3+614x^4+1080x^5+5453x^6+17916x^7+5453x^8+1080x^9+614x^10+202x^11+76x^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 0.0904 seconds.