The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+164x^5+721x^6+2806x^7+6760x^8+13922x^9+16767x^10+13932x^11+6796x^12+2808x^13+687x^14+158x^15+11x^16+2x^17+1x^18

The gray image is a linear code over GF(2) with n=40, k=16 and d=10.
This code was found by Heurico 1.13 in 0.453 seconds.