The generator matrix

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

generates a code of length 40 over Z2[X]/(X^3) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+272x^38+59x^40+128x^42+48x^46+3x^48+1x^56

The gray image is a linear code over GF(2) with n=160, k=9 and d=76.
As d=77 is an upper bound for linear (160,9,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 9.
This code was found by an older version of Heurico in 0 seconds.