The generator matrix

 1  0  1  1  1 X^2+X  1  1  1
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2 X^2+X  0
 0  0 X^3  0 X^3  0  0 X^3  0
 0  0  0 X^3 X^3 X^3 X^3 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+14x^6+64x^7+242x^8+384x^9+240x^10+64x^11+12x^12+2x^14+1x^16

The gray image is a linear code over GF(2) with n=72, k=10 and d=24.
This code was found by Heurico 1.16 in -1.01e-007 seconds.