The generator matrix

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

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+53x^4+32x^5+48x^6+160x^7+842x^8+1856x^9+2208x^10+1856x^11+842x^12+160x^13+48x^14+32x^15+53x^16+1x^20

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 0.0458 seconds.