The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+93x^20+31x^24+3x^28

The gray image is a linear code over GF(2) with n=84, k=7 and d=40.
As d=40 is an upper bound for linear (84,7,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 7.
This code was found by an older version of Heurico in 0 seconds.