The generator matrix

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

generates a code of length 11 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+79x^4+168x^6+1346x^8+2376x^10+2838x^12+1016x^14+333x^16+24x^18+11x^20

The gray image is a code over GF(2) with n=22, k=13 and d=4.
This code was found by Heurico 1.16 in 0.121 seconds.