The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+38x^77+6x^78+4x^79+6x^80+6x^81+1x^82+1x^84+1x^86

The gray image is a linear code over GF(2) with n=308, k=6 and d=154.
This code was found by Heurico 1.16 in 0.226 seconds.