The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+160x^65+135x^66+306x^67+206x^68+278x^69+199x^70+258x^71+109x^72+96x^73+45x^74+58x^75+24x^76+38x^77+14x^78+52x^79+28x^80+16x^81+6x^82+12x^83+4x^85+1x^86+2x^87

The gray image is a linear code over GF(2) with n=280, k=11 and d=130.
This code was found by Heurico 1.16 in 0.339 seconds.