The generator matrix

 1  0  0  0  0  1  1  1  1  0  1  1
 0  1  0  0  0  0  0  1  1  1  2  2
 0  0  1  0  0  0  1  0  1  3  2  0
 0  0  0  1  0  1  1  3  0  3  1  0
 0  0  0  0  1  1  0  2  0  2  2  1
 0  0  0  0  0  2  0  0  2  2  2  0
 0  0  0  0  0  0  2  2  2  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+52x^6+100x^7+158x^8+264x^9+508x^10+700x^11+644x^12+560x^13+428x^14+348x^15+217x^16+72x^17+36x^18+4x^19+4x^20

The gray image is a code over GF(2) with n=24, k=12 and d=6.
This code was found by Heurico 1.16 in 0.0555 seconds.