The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1 X^2  1  1  1  1  1  X  X
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X  0 X^2 X^2+X X^2+X  0 X^2  X X^2+X  X  0 X^2 X^2+X  0  0  X  X X^2  0  X  X  0 X^2  X  0 X^2  X X^2  X  0 X^2+X X^2 X^2+X  X X^2+X  0 X^2+X  X  X  0  X  0  X X^2+X X^2+X X^2  0 X^2  0 X^2 X^2+X  0 X^2 X^2 X^2+X X^2+X  X X^2  0
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0 X^2  X X^2+X X^2  0  X X^2+X  0  0 X^2 X^2+X  X  0 X^2+X  X X^2  0 X^2+X  X X^2  0  X  X X^2+X  0 X^2+X X^2+X  0  X  0  0  X X^2 X^2+X X^2 X^2  0 X^2+X  0 X^2+X X^2 X^2  0 X^2 X^2 X^2+X X^2+X  X X^2  0 X^2  X X^2 X^2+X  X  X  X  0
 0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2  0  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+57x^64+102x^66+64x^67+101x^68+128x^69+182x^70+64x^71+174x^72+70x^74+42x^76+26x^78+8x^80+4x^82+1x^132

The gray image is a linear code over GF(2) with n=280, k=10 and d=128.
This code was found by Heurico 1.16 in 0.289 seconds.