The generator matrix

 1  0  1  1  1  1  1  1  1  1  1
 0  1  1  0  0  0  0  0  0  0  0
 0  0  2  0  0  0  0  0  0  0  0
 0  0  0  2  0  0  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0
 0  0  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0
 0  0  0  0  0  0  0  0  0  0  2

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

Homogenous weight enumerator: w(x)=1x^0+15x^2+91x^4+309x^6+666x^8+3014x^10+3014x^12+666x^14+309x^16+91x^18+15x^20+1x^22

The gray image is a code over GF(2) with n=22, k=13 and d=2.
This code was found by Heurico 1.16 in 0.093 seconds.