The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+84x^4+32x^5+249x^6+320x^7+782x^8+992x^9+932x^10+1408x^11+932x^12+992x^13+782x^14+320x^15+249x^16+32x^17+84x^18+1x^22

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 0.126 seconds.