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  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  0

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

Homogenous weight enumerator: w(x)=1x^0+52x^4+96x^6+350x^8+504x^10+588x^12+272x^14+153x^16+24x^18+8x^20

The gray image is a code over GF(2) with n=22, k=11 and d=4.
This code was found by Heurico 1.16 in 0.00659 seconds.