The generator matrix

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

generates a code of length 6 over Z8 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+24x^1+234x^2+1272x^3+4815x^4+14064x^5+24716x^6+14064x^7+4815x^8+1272x^9+234x^10+24x^11+1x^12

The gray image is a code over GF(2) with n=24, k=16 and d=2.
This code was found by Heurico 1.16 in 0.385 seconds.