The generator matrix
1 0 0 1 1 1 1 1 2X
0 1 0 1 3X+2 3X+3 2 3X+1 0
0 0 1 1 X+1 X X 0 1
0 0 0 2 0 2X 2X+2 2X+2 2X+2
generates a code of length 9 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+226x^6+848x^7+3685x^8+6880x^9+3664x^10+848x^11+226x^12+6x^14
The gray image is a code over GF(2) with n=72, k=14 and d=24.
This code was found by Heurico 1.16 in 0.531 seconds.