The generator matrix

 1  1  1  1  1  1  1  1  2  2
 0  2  0  0  0  0  0  2  6  6
 0  0  2  0  0  0  2  0  2  2
 0  0  0  2  0  2  2  2  0  0
 0  0  0  0  2  2  0  0  2  2
 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

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

Homogenous weight enumerator: w(x)=1x^0+92x^4+560x^6+3046x^8+8992x^10+3036x^12+560x^14+97x^16

The gray image is a code over GF(2) with n=40, k=14 and d=8.
This code was found by Heurico 1.16 in 0.228 seconds.