The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1 X^2  X  X  1  1  1  1  0  1  1 X^2+X  1  1  1  1  1  1  0  1  1  X X^2+X X^2+X X^2+X  1  1  1  1  1  0  1  0 X^2  1  1  1  1  X  1  1  X  1  1  0 X^2 X^2 X^2  1  1 X^2+X  X  1  1 X^2+X  X  1  X X^2 X^2
 0  1  1 X^2+X X+1  1 X^2+1 X^2  1  X X^2+X+1  1  1  1  0  1 X^2+X X^2  1 X^2+X+1  X  1  1 X^2+X+1 X^2+X+1  1 X+1  0  1 X^2+1  X  1  1  1  1  0 X^2+X  0  1 X^2+X+1  1 X^2+X  1  1 X^2 X^2+X X+1 X^2+1  0 X^2 X^2+X X^2+X X+1 X^2+1  1  1  1  1 X^2  1  1 X^2+X  X  1  1  1 X^2+X+1  1  0  X
 0  0  X  0 X^2  0 X^2  X  X  X  X X^2+X  0  X  0 X^2+X X^2+X X^2+X  0 X^2  0 X^2+X X^2 X^2+X  X  X  0 X^2+X X^2+X  0 X^2+X X^2+X X^2  X X^2 X^2 X^2  X  0  0  X  X X^2 X^2 X^2 X^2 X^2+X X^2+X X^2 X^2  0  0 X^2+X  X X^2 X^2  0  X X^2+X  0 X^2+X X^2+X X^2+X X^2  X  0 X^2+X  X  X X^2
 0  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  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  0  0  0  0 X^2 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 67.

Homogenous weight enumerator: w(x)=1x^0+48x^67+195x^68+16x^69+49x^70+40x^71+98x^72+16x^73+10x^74+6x^75+25x^76+3x^78+1x^82+1x^88+1x^90+2x^91

The gray image is a linear code over GF(2) with n=280, k=9 and d=134.
This code was found by Heurico 1.16 in 36.1 seconds.