The generator matrix

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

generates a code of length 9 over Z2[X]/(X^4) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+20x^5+46x^6+64x^7+206x^8+1368x^9+220x^10+64x^11+32x^12+20x^13+6x^14+1x^16

The gray image is a linear code over GF(2) with n=72, k=11 and d=20.
This code was found by Heurico 1.16 in -3.24e-008 seconds.