The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+51x^4+90x^5+173x^6+300x^7+485x^8+1678x^9+2685x^10+1608x^11+457x^12+342x^13+207x^14+76x^15+30x^16+2x^17+7x^18

The gray image is a linear code over GF(2) with n=40, k=13 and d=8.
This code was found by Heurico 1.16 in 0.0627 seconds.