The generator matrix

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

generates a code of length 7 over Z8 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+18x^1+139x^2+628x^3+1881x^4+3982x^5+10267x^6+31704x^7+10267x^8+3982x^9+1881x^10+628x^11+139x^12+18x^13+1x^14

The gray image is a code over GF(2) with n=28, k=16 and d=2.
This code was found by Heurico 1.16 in 0.516 seconds.