The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1
 0  1  0  1  0  1  1  0  0  0
 0  0  1  1  1  0  1  0  0  0
 0  0  0  X  0  0  X X^2+X X^2+X  0
 0  0  0  0  X  0  X X^2+X  X  0
 0  0  0  0  0  X  X X^2 X^2  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+96x^4+108x^5+597x^6+1468x^7+3380x^8+6616x^9+8235x^10+6616x^11+3380x^12+1468x^13+603x^14+108x^15+87x^16+5x^18

The gray image is a linear code over GF(2) with n=40, k=15 and d=8.
This code was found by Heurico 1.16 in 0.587 seconds.