The generator matrix

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

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+72x^67+108x^68+82x^69+77x^70+46x^71+28x^72+38x^73+25x^74+6x^75+13x^76+8x^77+1x^80+1x^82+4x^83+1x^84+1x^86

The gray image is a linear code over GF(2) with n=280, k=9 and d=134.
This code was found by Heurico 1.11 in 0.078 seconds.