The generator matrix

 1  1  1  1  2 X^2+2  X  1  1
 0  X  0  X  X  X X^2+2 X^2+X  0
 0  0  X  X X^2 X^2+X X+2 X^2+X  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+10x^6+92x^7+193x^8+460x^9+156x^10+84x^11+22x^12+4x^13+2x^14

The gray image is a code over GF(2) with n=72, k=10 and d=24.
This code was found by Heurico 1.16 in -3.24e-008 seconds.