The generator matrix

 1  0  0  1  2  1  1
 0  1  0  1  0  0  0
 0  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

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

Homogenous weight enumerator: w(x)=1x^0+55x^2+96x^3+533x^4+1152x^5+4019x^6+4672x^7+4019x^8+1152x^9+533x^10+96x^11+55x^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 0.0506 seconds.