The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+52x^69+15x^70+32x^71+15x^72+4x^73+8x^75+1x^78

The gray image is a linear code over GF(2) with n=280, k=7 and d=138.
This code was found by Heurico 1.16 in 0.161 seconds.