The generator matrix

 1  1  1  1  2  2  1
 0  2  0 14  6  6  0
 0  0 12  4  8  8  0
 0  0  0  8  8  0  0

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

Homogenous weight enumerator: w(x)=1x^0+24x^4+90x^5+72x^6+654x^7+69x^8+86x^9+24x^10+2x^11+2x^12

The gray image is a code over GF(2) with n=56, k=10 and d=16.
This code was found by Heurico 1.16 in 0.000979 seconds.