The generator matrix

 1  0  1  2  1  1  1
 0  1  1  0  0  0  0
 0  0  2  2  0  0  0
 0  0  0  4  0  0  0
 0  0  0  0  4  0  0
 0  0  0  0  0  4  0
 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+27x^2+16x^3+121x^4+288x^5+875x^6+1440x^7+875x^8+288x^9+121x^10+16x^11+27x^12+1x^14

The gray image is a code over GF(2) with n=28, k=12 and d=4.
This code was found by Heurico 1.16 in 0.00389 seconds.