The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+151x^70+84x^71+281x^72+288x^73+460x^74+572x^75+632x^76+724x^77+621x^78+756x^79+577x^80+708x^81+555x^82+596x^83+403x^84+316x^85+189x^86+40x^87+98x^88+12x^89+52x^90+33x^92+13x^94+18x^96+5x^98+3x^100+2x^102+1x^104+1x^108

The gray image is a linear code over GF(2) with n=316, k=13 and d=140.
This code was found by Heurico 1.16 in 5.62 seconds.