The generator matrix

 1  0  1  1  1 X^2  1  1  1  0
 0  1  1  0  1  1 X^2+X+1 X+1  1  0
 0  0  X  0  0  0  X  X X^2+X X^2
 0  0  0  X  0  X  X X^2+X X^2  X
 0  0  0  0  X X^2 X^2+X  0 X^2+X 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+64x^6+288x^7+226x^8+1152x^9+448x^10+1472x^11+216x^12+128x^13+64x^14+32x^15+5x^16

The gray image is a linear code over GF(2) with n=40, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0298 seconds.