The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+120x^4+736x^6+3191x^8+7328x^10+10016x^12+7328x^14+3191x^16+736x^18+120x^20+1x^24

The gray image is a code over GF(2) with n=24, k=15 and d=4.
This code was found by Heurico 1.16 in 2.73 seconds.