The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+12x^22+3x^24

The gray image is a linear code over GF(2) with n=84, k=4 and d=44.
As d=44 is an upper bound for linear (84,4,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 4.
This code was found by Heurico 1.16 in 0.00184 seconds.