The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+30x^6+97x^8+97x^10+30x^12+1x^18

The gray image is a linear code over GF(2) with n=36, k=8 and d=12.
This code was found by Heurico 1.16 in 0.000553 seconds.