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  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  0

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

Homogenous weight enumerator: w(x)=1x^0+44x^4+40x^6+215x^8+344x^10+760x^12+344x^14+215x^16+40x^18+44x^20+1x^24

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 0.00786 seconds.