The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  0  0  0  1  1  1  1  X  X  X  0  0  0  1  1  1  1  X  0  X  0  X  0  X  1  1  1  1  X  X  0  X  0  X  0  X  1  1  1  1  X  X  X  X  0  0  0  X  X  X  X  X  1
 0  X  0  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  X  0  X  X  X  X  0  0  0  X  X  0  0  X  X  X  X  0  0  0  X  X  0  0  0  X  X  X  X  0  0  0  X  X  0  0  X  X  X  X  0  0  0  X  X  0  0
 0  0  X  X  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  0  0  X  X  0  X  X  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  X  X  0  0  0  0  X  X  0  0  X  X  0  0  X  X  0  X  X  0  0  0

generates a code of length 84 over Z2[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+3x^88+6x^89+4x^90+2x^93

The gray image is a linear code over GF(2) with n=168, k=4 and d=88.
As d=88 is an upper bound for linear (168,4,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 4.
This code was found by Heurico 1.16 in 0.106 seconds.