The generator matrix

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

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+70x^5+377x^6+1392x^7+3332x^8+7238x^9+7935x^10+7248x^11+3348x^12+1394x^13+359x^14+64x^15+7x^16+2x^17+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 1.16 in 0.766 seconds.