The generator matrix

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

generates a code of length 12 over Z4 who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+48x^5+145x^6+340x^7+746x^8+1244x^9+1828x^10+2484x^11+2736x^12+2428x^13+1862x^14+1244x^15+733x^16+372x^17+132x^18+28x^19+8x^20+4x^21+1x^22

The gray image is a code over GF(2) with n=24, k=14 and d=5.
This code was found by Heurico 1.16 in 1.31 seconds.