The generator matrix

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

generates a code of length 77 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+381x^70+240x^71+819x^72+340x^73+1072x^74+300x^75+1046x^76+388x^77+911x^78+300x^79+737x^80+204x^81+547x^82+164x^83+356x^84+76x^85+172x^86+20x^87+75x^88+16x^89+21x^90+2x^92+4x^96

The gray image is a linear code over GF(2) with n=308, k=13 and d=140.
This code was found by Heurico 1.11 in 9.88 seconds.