The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+109x^6+342x^7+915x^8+1680x^9+2050x^10+1772x^11+906x^12+288x^13+113x^14+14x^15+2x^16

The gray image is a linear code over GF(2) with n=40, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0924 seconds.