The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+61x^4+152x^5+323x^6+880x^7+1642x^8+2608x^9+3828x^10+4528x^11+4698x^12+4576x^13+3794x^14+2640x^15+1621x^16+848x^17+372x^18+144x^19+41x^20+8x^21+3x^22

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 1.95 seconds.