The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+113x^4+68x^5+553x^6+490x^7+1485x^8+2032x^9+1953x^10+3022x^11+1925x^12+2004x^13+1491x^14+518x^15+566x^16+56x^17+99x^18+2x^19+6x^20

The gray image is a code over GF(2) with n=22, k=14 and d=4.
This code was found by Heurico 1.16 in 0.971 seconds.