The generator matrix
1 1 1 1 2 1
0 12 0 4 8 0
0 0 12 4 4 8
generates a code of length 6 over Z16 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+9x^4+34x^5+173x^6+28x^7+6x^8+2x^9+3x^10
The gray image is a code over GF(2) with n=48, k=8 and d=16.
This code was found by Heurico 1.16 in 0.00022 seconds.