The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+94x^65+523x^66+996x^67+1780x^68+2492x^69+3886x^70+4462x^71+6736x^72+7170x^73+9745x^74+9804x^75+11846x^76+11310x^77+12230x^78+9898x^79+10185x^80+7538x^81+7037x^82+4348x^83+3572x^84+2104x^85+1362x^86+866x^87+522x^88+254x^89+151x^90+84x^91+42x^92+14x^93+10x^94+6x^95+4x^96

The gray image is a linear code over GF(2) with n=308, k=17 and d=130.
This code was found by Heurico 1.13 in 246 seconds.