The generator matrix

 1  1  1  1  2  2  1
 0  2 12  6  6  6  0
 0  0  8  0  0  8  0
 0  0  0  8  0  8  0
 0  0  0  0  8  8  0

generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+18x^4+96x^5+109x^6+576x^7+109x^8+96x^9+18x^10+1x^14

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 0.000794 seconds.