The generator matrix

 1  0  0  0  1  1  1  0  0  0  1  1  1  1  X  1  1  1  1  X  1  X  X  1  1  0  1  1  X  1  0  1  X  X  0  1  1  1  0
 0  1  0  0  X  1 X+1  1  1  1  0  1  X X+1  1  0 X+1  1  0  1 X+1  0  X  0  1  X  X X+1  1  X  0  X  0  X  X  1  X X+1  0
 0  0  1  0  0  0  0  X  1 X+1  1  1 X+1  1  X  X  X X+1 X+1  1 X+1  1  1  X  1  1  0 X+1  0  X  1  1  1  1  1  X  X  1  0
 0  0  0  1  1 X+1  X X+1  1  X  1  X  X X+1  X  X  0  1 X+1  1  1 X+1 X+1  1  0  1 X+1  X  0  1  X  0  0  X X+1  0  X  1  1

generates a code of length 39 over Z2[X]/(X^2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+89x^36+72x^38+38x^40+18x^42+22x^44+4x^46+3x^48+2x^50+5x^52+2x^56

The gray image is a linear code over GF(2) with n=78, k=8 and d=36.
As d=36 is an upper bound for linear (78,8,2)-codes, this code is optimal over Z2[X]/(X^2) for dimension 8.
This code was found by Heurico 1.16 in 0.017 seconds.