The generator matrix

 1  0  1  1  1  0  2
 0  1  3  6  5  1  0
 0  0  8  0  0  0  8
 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+45x^4+224x^5+712x^6+2112x^7+747x^8+224x^9+24x^10+7x^12

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00375 seconds.