The generator matrix

 1  0  1  1  1  0  1  1  1  1  2  1
 0  1  1  0  1  1  0  0  0  0  0  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+53x^4+58x^6+338x^8+256x^9+328x^10+768x^11+450x^12+768x^13+460x^14+256x^15+173x^16+168x^18+9x^20+10x^22

The gray image is a code over GF(2) with n=24, k=12 and d=4.
This code was found by Heurico 1.16 in 0.0355 seconds.