The generator matrix
1 1 1 1 2 2 1
0 12 0 4 8 4 0
0 0 12 4 4 12 8
generates a code of length 7 over Z16 who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+14x^5+34x^6+166x^7+23x^8+10x^9+6x^10+2x^11
The gray image is a code over GF(2) with n=56, k=8 and d=20.
This code was found by Heurico 1.16 in 0.00035 seconds.