The generator matrix

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

generates a code of length 10 over Z4 who´s minimum homogenous weight is 3.

Homogenous weight enumerator: w(x)=1x^0+12x^3+57x^4+138x^5+291x^6+600x^7+947x^8+1230x^9+1451x^10+1388x^11+1019x^12+614x^13+305x^14+112x^15+24x^16+2x^17+1x^18

The gray image is a code over GF(2) with n=20, k=13 and d=3.
This code was found by Heurico 1.10 in 0.00487 seconds.