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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+28x^69+78x^70+14x^72+4x^77+1x^78+1x^80+1x^94

The gray image is a linear code over GF(2) with n=280, k=7 and d=138.
This code was found by Heurico 1.16 in 0.203 seconds.