The generator matrix

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

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+109x^70+100x^71+338x^72+324x^73+500x^74+496x^75+571x^76+764x^77+645x^78+744x^79+606x^80+740x^81+494x^82+496x^83+369x^84+340x^85+214x^86+84x^87+112x^88+8x^89+55x^90+30x^92+28x^94+18x^96+3x^98+2x^100+1x^104

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 5.2 seconds.