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

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+32x^64+62x^65+75x^66+78x^67+95x^68+134x^69+118x^70+122x^71+102x^72+62x^73+47x^74+28x^75+23x^76+10x^77+11x^78+10x^79+3x^80+4x^81+4x^82+2x^83+1x^126

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 0.285 seconds.