The generator matrix

 1  0  0  0  1  1
 0  1  0  0  3  0
 0  0  1  0  1  0
 0  0  0  1  1  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+78x^2+288x^3+1215x^4+3552x^5+6116x^6+3552x^7+1215x^8+288x^9+78x^10+1x^12

The gray image is a code over GF(2) with n=24, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0442 seconds.