The generator matrix

 1  0  1  1  1  0  0
 0  1 11 14  5  1  1
 0  0 12  4  0  0  8
 0  0  0  8  0  8  8
 0  0  0  0  8  8  8

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

Homogenous weight enumerator: w(x)=1x^0+74x^4+64x^5+821x^6+2176x^7+821x^8+64x^9+74x^10+1x^14

The gray image is a code over GF(2) with n=56, k=12 and d=16.
This code was found by Heurico 1.16 in 0.00323 seconds.