The generator matrix

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

generates a code of length 9 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+78x^8+32x^10+16x^12+1x^16

The gray image is a linear code over GF(2) with n=36, k=7 and d=16.
As d=16 is an upper bound for linear (36,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by Heurico 1.16 in 0.000373 seconds.