The generator matrix

 1  1  1  1  X  0  1  1  1
 0  X  0 X^2+X X^2+X  X X^2 X^3+X^2 X^3
 0  0 X^3+X^2  0  0 X^3 X^2 X^3 X^2
 0  0  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3 X^3  0  0 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+44x^6+80x^7+598x^8+608x^9+592x^10+80x^11+40x^12+4x^14+1x^16

The gray image is a linear code over GF(2) with n=72, k=11 and d=24.
This code was found by Heurico 1.16 in 6.87e-008 seconds.