The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  1  1
 0  1 X+1 X^3+X^2+X X^2+1  1  0 X^2+X  0
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0
 0  0  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 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+61x^6+172x^7+965x^8+1708x^9+958x^10+164x^11+58x^12+4x^13+5x^14

The gray image is a linear code over GF(2) with n=72, k=12 and d=24.
This code was found by Heurico 1.16 in 0.016 seconds.