The generator matrix

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

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+60x^64+198x^65+219x^66+256x^67+42x^68+236x^69+150x^70+222x^71+78x^72+164x^73+138x^74+134x^75+36x^76+36x^77+26x^78+18x^79+5x^80+6x^81+10x^82+10x^83+1x^98+2x^100

The gray image is a linear code over GF(2) with n=280, k=11 and d=128.
This code was found by Heurico 1.16 in 0.435 seconds.