The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+148x^4+560x^6+1374x^8+4096x^9+1248x^10+644x^12+112x^14+9x^16

The gray image is a linear code over GF(2) with n=36, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0644 seconds.