The generator matrix

 1  0  1  1  1  2  2  2  2  1
 0  1  1  2  3  1  0  2  0  0
 0  0  2  0  2  0  2  2  0  0

generates a code of length 10 over Z4 who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+7x^8+4x^9+7x^10+8x^11+4x^13+1x^18

The gray image is a code over GF(2) with n=20, k=5 and d=8.
This code was found by Heurico 1.16 in 0.000185 seconds.