The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+115x^2+240x^3+2465x^4+5184x^5+15851x^6+17824x^7+15851x^8+5184x^9+2465x^10+240x^11+115x^12+1x^14

The gray image is a code over GF(2) with n=28, k=16 and d=4.
This code was found by Heurico 1.16 in 0.771 seconds.