The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+56x^2+940x^4+4536x^6+10902x^8+16312x^10+16396x^12+10824x^14+4593x^16+912x^18+64x^20

The gray image is a code over GF(2) with n=22, k=16 and d=2.
This code was found by Heurico 1.10 in 0.0429 seconds.