The generator matrix

 1  0  0  0  0  0  1  1  1  1  1  2
 0  1  0  0  0  0  0  1  0  2  3  1
 0  0  1  0  0  0  0  1  2  3  0  1
 0  0  0  1  0  0  0  1  3  1  1  1
 0  0  0  0  1  0  1  1  2  0  3  0
 0  0  0  0  0  1  1  2  3  2  0  1
 0  0  0  0  0  0  2  0  0  2  2  0

generates a code of length 12 over Z4 who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+152x^6+714x^8+1888x^10+2672x^12+1912x^14+701x^16+144x^18+8x^20

The gray image is a code over GF(2) with n=24, k=13 and d=6.
This code was found by Heurico 1.16 in 0.276 seconds.