The generator matrix

 1  0  1  1  1 14  1
 0  1 11  6  5  1  0
 0  0 12  0  4  8  0
 0  0  0 12  4 12  8

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

Homogenous weight enumerator: w(x)=1x^0+26x^4+160x^5+869x^6+1984x^7+869x^8+160x^9+26x^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 0.00348 seconds.