The generator matrix

 1  0  1  1  1 X^2+X  1  1  X  1
 0  1  1  0 X+1  1  X  0 X^2  0
 0  0  X X^2+X  0  0 X^2+X X^2  X  0
 0  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0 X^2 X^2 X^2 X^2  0 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+16x^6+48x^7+97x^8+260x^9+157x^10+300x^11+94x^12+28x^13+18x^14+4x^15+1x^18

The gray image is a linear code over GF(2) with n=40, k=10 and d=12.
This code was found by Heurico 1.16 in 0.00245 seconds.