The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 2.

Homogenous weight enumerator: w(x)=1x^0+24x^2+186x^4+760x^6+1935x^8+6384x^10+14188x^12+6384x^14+1935x^16+760x^18+186x^20+24x^22+1x^24

The gray image is a code over GF(2) with n=24, k=15 and d=2.
This code was found by Heurico 1.16 in 0.86 seconds.