The generator matrix

 1  0  1  1  1  8  0
 0  1  1 12 11  1  1
 0  0  2  6  4  4  0
 0  0  0  8  0  8  8
 0  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+122x^4+224x^5+1541x^6+4416x^7+1541x^8+224x^9+122x^10+1x^14

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 0.0102 seconds.