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  4  0
 0  0  0  0  2  4  0

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

Homogenous weight enumerator: w(x)=1x^0+52x^2+106x^3+254x^4+600x^5+1485x^6+3196x^7+1485x^8+600x^9+254x^10+106x^11+52x^12+1x^14

The gray image is a code over GF(2) with n=28, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0158 seconds.