The generator matrix

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

generates a code of length 79 over Z2[X]/(X^3) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+120x^71+248x^72+460x^73+408x^74+822x^75+504x^76+820x^77+451x^78+936x^79+455x^80+710x^81+406x^82+600x^83+275x^84+360x^85+180x^86+188x^87+94x^88+72x^89+18x^90+18x^91+18x^92+4x^93+9x^94+4x^95+2x^96+6x^97+3x^100

The gray image is a linear code over GF(2) with n=316, k=13 and d=142.
This code was found by Heurico 1.16 in 4.65 seconds.