The generator matrix

 1  0  1  1  1  8  2
 0  1 11  6  5  1  8
 0  0 12  0  0  8  4
 0  0  0 12  0  4  8
 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+109x^4+288x^5+1928x^6+3520x^7+1963x^8+288x^9+88x^10+7x^12

The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.0138 seconds.