The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+32x^3+189x^4+480x^5+1120x^6+2464x^7+4034x^8+5216x^9+5696x^10+5216x^11+4034x^12+2464x^13+1120x^14+480x^15+189x^16+32x^17+1x^20

The gray image is a code over GF(2) with n=20, k=15 and d=3.
This code was found by Heurico 1.10 in 0.0195 seconds.