The generator matrix

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

generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+30x^6+161x^8+128x^9+161x^10+30x^12+1x^18

The gray image is a linear code over GF(2) with n=72, k=9 and d=24.
This code was found by Heurico 1.16 in 3.81e-009 seconds.