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
 0  0  0  0  0  4

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

Homogenous weight enumerator: w(x)=1x^0+26x^2+16x^3+207x^4+368x^5+812x^6+368x^7+207x^8+16x^9+26x^10+1x^12

The gray image is a code over GF(2) with n=24, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00142 seconds.