The generator matrix

 1  0  0  0  0  0  0  1  1  1  1
 0  1  0  0  0  0  0  1  2  2  2
 0  0  1  0  0  0  0  1  0  0  2
 0  0  0  1  0  0  0  1  0  2  2
 0  0  0  0  1  0  0  1  1  3  3
 0  0  0  0  0  1  0  1  3  1  3
 0  0  0  0  0  0  1  1  3  1  1
 0  0  0  0  0  0  0  2  2  0  2

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

Homogenous weight enumerator: w(x)=1x^0+164x^4+64x^5+808x^6+896x^7+2726x^8+4032x^9+4472x^10+6400x^11+4556x^12+4032x^13+2648x^14+896x^15+865x^16+64x^17+136x^18+8x^20

The gray image is a code over GF(2) with n=22, k=15 and d=4.
This code was found by Heurico 1.16 in 2.25 seconds.