The generator matrix

 1  0  0  0  0  0  1  1  1  1  1
 0  1  0  0  0  0  0  1  2  2  0
 0  0  1  0  0  0  0  1  0  1  2
 0  0  0  1  0  0  1  0  0  1  2
 0  0  0  0  1  0  1  0  0  2  0
 0  0  0  0  0  1  1  1  1  3  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+53x^4+92x^5+262x^6+696x^7+1180x^8+2020x^9+2614x^10+2576x^11+2572x^12+2020x^13+1186x^14+696x^15+283x^16+92x^17+34x^18+7x^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 0.984 seconds.