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.