The generator matrix

 1  0  1  1  1  0  2
 0  1 11 14  5  1  8
 0  0 12  4  0 12  4
 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+93x^4+384x^5+1688x^6+3840x^7+1723x^8+384x^9+72x^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 0.013 seconds.