The generator matrix

 1  1  1  1  1  1  1  1  X  1
 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  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+28x^4+8x^6+70x^8+128x^9+568x^10+128x^11+28x^12+56x^14+1x^16+8x^18

The gray image is a linear code over GF(2) with n=40, k=10 and d=8.
This code was found by Heurico 1.16 in 0.00155 seconds.