The generator matrix

 1  1  1  1  1  1  1  1  X
 0 X^3+X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2
 0  0 X^3+X^2  0 X^3+X^2 X^3+X^2 X^2 X^3 X^2
 0  0  0 X^3+X^2 X^2 X^3 X^2 X^2  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+20x^6+64x^7+110x^8+640x^9+104x^10+64x^11+16x^12+4x^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 0.015 seconds.