The generator matrix

 1  0  1  1  1 12  2
 0  1  1 12 11  1  4
 0  0  2  6  4  6  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+864x^5+3432x^6+7488x^7+3467x^8+864x^9+120x^10+7x^12

The gray image is a code over GF(2) with n=56, k=14 and d=16.
This code was found by Heurico 1.16 in 0.0483 seconds.