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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+20x^66+36x^67+61x^68+102x^69+88x^70+76x^71+63x^72+40x^73+20x^74+2x^76+2x^77+1x^124

The gray image is a linear code over GF(2) with n=280, k=9 and d=132.
This code was found by Heurico 1.16 in 0.224 seconds.