The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+38x^5+97x^6+144x^7+228x^8+326x^9+367x^10+336x^11+244x^12+146x^13+79x^14+32x^15+7x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=20, k=11 and d=5.
This code was found by Heurico 1.10 in 0.016 seconds.