The generator matrix

 1  0  0  1  1  1  4
 0  1  0  1  6 12  1
 0  0  1  1  3  1  2
 0  0  0 12  0  4  8

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

Homogenous weight enumerator: w(x)=1x^0+92x^4+736x^5+3352x^6+8008x^7+3385x^8+720x^9+80x^10+8x^11+2x^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 0.094 seconds.