The generator matrix
1 0 1 1 1 0 2
0 1 11 14 5 1 8
0 0 12 4 0 12 4
0 0 0 8 0 0 8
0 0 0 0 8 0 8
0 0 0 0 0 8 8
generates a code of length 7 over Z16 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+93x^4+384x^5+1688x^6+3840x^7+1723x^8+384x^9+72x^10+7x^12
The gray image is a code over GF(2) with n=56, k=13 and d=16.
This code was found by Heurico 1.16 in 0.013 seconds.