The generator matrix

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

generates a code of length 78 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+103x^70+312x^71+375x^72+546x^73+517x^74+786x^75+623x^76+758x^77+561x^78+752x^79+491x^80+642x^81+385x^82+436x^83+292x^84+220x^85+138x^86+102x^87+65x^88+24x^89+18x^90+6x^91+9x^92+18x^93+6x^94+6x^95

The gray image is a linear code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 4.31 seconds.