The generator matrix

 1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0 X^3  0  0 X^3
 0  0 X^3  0  0 X^3  0 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3  0  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+6x^6+9x^8+224x^9+9x^10+6x^12+1x^18

The gray image is a linear code over GF(2) with n=72, k=8 and d=24.
This code was found by Heurico 1.16 in 6.87e-008 seconds.