The generator matrix

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

generates a code of length 4 over Z8 who´s minimum homogenous weight is 1.

Homogenous weight enumerator: w(x)=1x^0+12x^1+52x^2+180x^3+534x^4+180x^5+52x^6+12x^7+1x^8

The gray image is a code over GF(2) with n=16, k=10 and d=2.
This code was found by Heurico 1.16 in 0.000284 seconds.