The generator matrix

1 0 0 0 0 0 0 1 1 1
0 1 0 0 0 0 0 1 0 0
0 0 1 0 0 0 0 1 0 0
0 0 0 1 0 0 0 1 0 0
0 0 0 0 1 0 0 1 0 0
0 0 0 0 0 1 0 1 0 0
0 0 0 0 0 0 1 1 0 0

generates a code of length 10 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+42x^2+525x^4+1848x^6+3570x^8+4412x^10+3570x^12+1848x^14+525x^16+42x^18+1x^20

The gray image is a code over GF(2) with n=20, k=14 and d=2.
This code was found by Heurico 1.10 in 0.0045 seconds.