The generator matrix

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

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+23x^6+24x^7+139x^8+148x^9+132x^10+16x^11+20x^12+4x^13+5x^14

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 1.05e-007 seconds.