The generator matrix

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

generates a code of length 10 over Z8 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+14x^2+77x^4+232x^6+434x^8+2048x^9+2580x^10+2048x^11+434x^12+232x^14+77x^16+14x^18+1x^20

The gray image is a code over GF(2) with n=40, k=13 and d=4.
This code was found by Heurico 1.16 in 0.0265 seconds.