The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+154x^64+362x^65+332x^66+462x^67+398x^68+424x^69+336x^70+338x^71+266x^72+204x^73+187x^74+160x^75+122x^76+120x^77+74x^78+74x^79+43x^80+26x^81+7x^82+6x^83

The gray image is a linear code over GF(2) with n=280, k=12 and d=128.
This code was found by Heurico 1.11 in 0.344 seconds.