The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  1
 0  1  0  0  0  0  1  1  1  0  2  0
 0  0  1  0  0  1  1  0  1  0  0  0
 0  0  0  1  0  1  0  1  1  0  0  0
 0  0  0  0  1  1  0  0  0  1  1  0
 0  0  0  0  0  2  0  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  2  0
 0  0  0  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  0
 0  0  0  0  0  0  0  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+109x^4+24x^5+522x^6+520x^7+2130x^8+2392x^9+3448x^10+5256x^11+3922x^12+5256x^13+3580x^14+2392x^15+1965x^16+520x^17+632x^18+24x^19+65x^20+10x^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 1.67 seconds.