The generator matrix

 1  1  1  1  1  1  1
 0 12  0  0  8 12  0
 0  0 12  0 12 12  8
 0  0  0 12  4  8  0

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

Homogenous weight enumerator: w(x)=1x^0+26x^4+32x^5+37x^6+832x^7+37x^8+32x^9+26x^10+1x^14

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 0.000887 seconds.