The generator matrix

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

generates a code of length 10 over Z8 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+69x^4+272x^6+1850x^8+3808x^10+1850x^12+272x^14+69x^16+1x^20

The gray image is a code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0657 seconds.