The generator matrix

 1  0  0  1  1  1  2
 0  1  0  2  5  7  1
 0  0  1  1  3  2  1
 0  0  0  8  0  0  8
 0  0  0  0  8  0  8
 0  0  0  0  0  8  8

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

Homogenous weight enumerator: w(x)=1x^0+77x^4+2016x^5+5544x^6+17472x^7+5579x^8+2016x^9+56x^10+7x^12

The gray image is a code over GF(2) with n=56, k=15 and d=16.
This code was found by Heurico 1.16 in 0.152 seconds.