The generator matrix

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

generates a code of length 7 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+69x^2+164x^3+619x^4+1392x^5+2895x^6+6104x^7+2895x^8+1392x^9+619x^10+164x^11+69x^12+1x^14

The gray image is a code over GF(2) with n=28, k=14 and d=4.
This code was found by Heurico 1.16 in 0.0505 seconds.