The generator matrix
1 1 1 1
0 12 0 8
0 0 12 8
generates a code of length 4 over Z16 who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+8x^2+16x^3+206x^4+16x^5+8x^6+1x^8
The gray image is a code over GF(2) with n=32, k=8 and d=8.
This code was found by Heurico 1.16 in 7.61e-005 seconds.