The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+36x^4+9x^6+126x^8+84x^10+512x^11+84x^12+126x^14+9x^16+36x^18+1x^22

The gray image is a code over GF(2) with n=22, k=10 and d=4.
This code was found by Heurico 1.16 in 0.00299 seconds.