The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+55x^6+48x^7+302x^8+208x^9+811x^10+208x^11+328x^12+48x^13+29x^14+9x^16+1x^18

The gray image is a linear code over GF(2) with n=40, k=11 and d=12.
This code was found by Heurico 1.16 in 0.0379 seconds.