The generator matrix

 1  0  0  0  1  1  1  1  1  1  1
 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  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+35x^2+287x^4+1141x^6+3706x^8+11214x^10+11214x^12+3706x^14+1141x^16+287x^18+35x^20+1x^22

The gray image is a code over GF(2) with n=22, k=15 and d=2.
This code was found by Heurico 1.16 in 0.784 seconds.