The generator matrix

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

generates a code of length 10 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+13x^8+56x^9+9x^10+32x^11+2x^12+8x^13+6x^14+1x^18

The gray image is a linear code over GF(2) with n=40, k=7 and d=16.
This code was found by Heurico 1.16 in 0.000427 seconds.