The generator matrix
1 0 1 1 1 1
0 1 3 6 0 6
0 0 4 0 4 0
0 0 0 4 4 0
generates a code of length 6 over Z8 who´s minimum homogenous weight is 4.
Homogenous weight enumerator: w(x)=1x^0+26x^4+48x^5+108x^6+48x^7+21x^8+4x^10
The gray image is a code over GF(2) with n=24, k=8 and d=8.
This code was found by Heurico 1.16 in 0.000176 seconds.