The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+42x^5+157x^6+360x^7+706x^8+1200x^9+1880x^10+2584x^11+2688x^12+2276x^13+1914x^14+1368x^15+693x^16+320x^17+144x^18+40x^19+8x^20+2x^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 1.19 seconds.