The generator matrix

 1  1  1  1  1  1  1
 0  2  0  0  4 14 10
 0  0  2  0  6  6  6
 0  0  0  2  2  4  6

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

Homogenous weight enumerator: w(x)=1x^0+154x^4+224x^5+1253x^6+4928x^7+1253x^8+224x^9+154x^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 0.33 seconds.