The generator matrix

 1  0  0  0  1  1  1  1  1
 0  1  0  0 X^2  1 X^2+X+1 X^2+X+1 X+1
 0  0  1  0 X^2+1 X+1  X  0 X+1
 0  0  0  1  1  X X+1  X  0
 0  0  0  0 X^3  0  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+144x^5+1336x^6+7552x^7+29118x^8+54752x^9+29152x^10+7552x^11+1312x^12+144x^13+8x^14+1x^16

The gray image is a linear code over GF(2) with n=72, k=17 and d=20.
This code was found by Heurico 1.16 in 6.02 seconds.