The generator matrix

 1  0  1  1  1  0  1  1  1  1  1  1
 0  1  1  0  1  1  0  0  0  0  0  0
 0  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

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

Homogenous weight enumerator: w(x)=1x^0+74x^4+64x^6+719x^8+1472x^10+3532x^12+1472x^14+719x^16+64x^18+74x^20+1x^24

The gray image is a code over GF(2) with n=24, k=13 and d=4.
This code was found by Heurico 1.16 in 0.158 seconds.