The generator matrix

 1  1  1  1  2  0  2
 0  2  0  2  2  2  4
 0  0  2  2  6 12  2
 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+141x^4+480x^5+1896x^6+3136x^7+1931x^8+480x^9+120x^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 0.0171 seconds.