The generator matrix

 1  0  1  1  1 X^2+X  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^2+3 X+1 X+3
 0  0 X^2  0  0  2 X^2+2  2 X^2
 0  0  0  2  0  2  2  0  0
 0  0  0  0  2  0  0  2  2

generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+60x^6+144x^7+1094x^8+1504x^9+1088x^10+144x^11+56x^12+4x^14+1x^16

The gray image is a code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 1.05e-007 seconds.