The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^4+512x^6+3247x^8+7168x^10+10684x^12+7168x^14+3247x^16+512x^18+114x^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 1.59 seconds.