The generator matrix

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

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+76x^5+393x^6+1180x^7+4036x^8+5912x^9+9567x^10+5912x^11+4052x^12+1180x^13+375x^14+76x^15+7x^16+1x^18

The gray image is a linear code over GF(2) with n=40, k=15 and d=10.
This code was found by Heurico 1.13 in 0.25 seconds.