The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+55x^6+92x^7+160x^8+304x^9+482x^10+620x^11+670x^12+640x^13+440x^14+308x^15+191x^16+80x^17+46x^18+4x^19+2x^20+1x^22

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 0.0691 seconds.