The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+148x^78+73x^80+28x^82+2x^84+2x^88+1x^92+1x^108

The gray image is a linear code over GF(2) with n=316, k=8 and d=156.
This code was found by Heurico 1.16 in 3.69 seconds.