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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+1x^82+12x^83+1x^84+1x^86

The gray image is a linear code over GF(2) with n=312, k=4 and d=164.
This code was found by Heurico 1.16 in 0.228 seconds.