The generator matrix

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

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+20x^6+72x^7+266x^8+424x^9+464x^10+472x^11+240x^12+56x^13+28x^14+5x^16

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 0.00815 seconds.