The generator matrix
1 1 1 1 1 1 2
0 8 0 0 0 0 8
0 0 8 0 0 0 8
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+21x^4+32x^6+384x^7+67x^8+7x^12
The gray image is a code over GF(2) with n=56, k=9 and d=16.
This code was found by Heurico 1.16 in 0.000349 seconds.