The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  X  X  X  1  1  X  X  1  1  X
 0 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^3+X^2  0
 0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3 X^3

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+18x^20+96x^21+6x^22+5x^24+2x^30

The gray image is a linear code over GF(2) with n=168, k=7 and d=80.
As d=83 is an upper bound for linear (168,7,2)-codes, this code is optimal over Z2[X]/(X^4) for dimension 7.
This code was found by Heurico 1.16 in 0 seconds.