The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^3+94x^4+238x^5+570x^6+1178x^7+1968x^8+2654x^9+2930x^10+2654x^11+1954x^12+1178x^13+590x^14+238x^15+79x^16+26x^17+6x^18

The gray image is a code over GF(2) with n=20, k=14 and d=3.
This code was found by Heurico 1.10 in 0.0204 seconds.