The generator matrix

 1  0  1  2  1  1
 0  1  1  0  0  0
 0  0  2  2  0  0
 0  0  0  4  0  0
 0  0  0  0  4  0

generates a code of length 6 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+24x^2+16x^3+103x^4+176x^5+384x^6+176x^7+103x^8+16x^9+24x^10+1x^12

The gray image is a code over GF(2) with n=24, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00046 seconds.