The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+45x^4+10x^6+210x^8+120x^10+512x^11+210x^12+512x^13+252x^14+45x^16+120x^18+1x^20+10x^22

The gray image is a code over GF(2) with n=24, k=11 and d=4.
This code was found by Heurico 1.16 in 0.0109 seconds.