The generator matrix

 1  0  0  1  1  1  0  0  1  1 X^2  1  1  0  1  1 X^2  1  1 X^2  1  1 X^2+X X^2+X  1  1  X  X  1  1  X  1  1  0 X^2  1  1  1 X^2+X  1  0  1  1  1 X^2+X  0  1  0 X^2  1  1  X  1  0  1  0  1  X  X  1  X  1 X^2+X X^2+X  1  1 X^2+X X^2  1  1
 0  1  0  0  1  1  1  0 X^2 X^2+1  1  0  1  1 X^2 X^2+1  1 X^2 X^2+1  1  0 X+1  1  0  0 X^2+X+1  1  0  X  X  X X^2  1  1  1 X^2+1 X^2+X+1  X  1 X^2+X+1 X^2+X X+1 X^2+X X^2+1  1  X X^2  1  1 X^2+X X^2+X X^2  X X^2+X X^2+X+1  1  1  1  1  X  1  1  1  1  X X^2  X  X X+1 X^2+X
 0  0  1  1 X^2 X^2+1  1  1  0 X^2  0  1 X^2+1  1 X^2  0 X^2 X^2  0 X^2 X+1 X^2+X+1  1  1 X^2+X+1 X+1  1  1  X  1  1  X X+1 X^2+X+1  X X^2+X  X  X X^2+X+1 X^2+1  1  X  1 X+1 X^2+X  1  X X+1 X^2+X  0 X^2+X  1 X+1  1  0  1 X+1  X X^2+1 X^2 X^2  X X+1 X+1 X^2+X X^2+1  1  1  1 X^2+X
 0  0  0  X  0  X  X X^2+X  X  X  X X^2 X^2 X^2 X^2 X^2 X^2 X^2+X X^2+X X^2+X X^2  0  0 X^2+X X^2+X  X X^2+X  0  0 X^2+X  0 X^2+X X^2+X X^2+X X^2 X^2 X^2+X  X  X  0 X^2+X X^2  0  0 X^2+X  0 X^2 X^2  0  X X^2+X X^2  0  X X^2  0  X X^2  X X^2  X  X  X X^2 X^2  0 X^2+X  X  X  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+144x^66+314x^67+209x^68+256x^69+164x^70+270x^71+126x^72+106x^73+49x^74+50x^75+28x^76+44x^77+24x^78+34x^79+18x^80+26x^81+1x^82+20x^83+1x^84+2x^86+1x^88

The gray image is a linear code over GF(2) with n=280, k=11 and d=130.
This code was found by Heurico 1.11 in 0.187 seconds.