The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+23x^4+96x^5+32x^6+224x^7+717x^8+1920x^9+696x^10+224x^11+53x^12+96x^13+8x^14+6x^16

The gray image is a linear code over GF(2) with n=72, k=12 and d=16.
This code was found by Heurico 1.16 in 0.015 seconds.