The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+48x^4+116x^5+332x^6+1052x^7+341x^8+108x^9+44x^10+4x^11+2x^12

The gray image is a code over GF(2) with n=56, k=11 and d=16.
This code was found by Heurico 1.16 in 0.00221 seconds.