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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+131x^60+4x^61+368x^62+32x^63+590x^64+144x^65+730x^66+328x^67+935x^68+500x^69+888x^70+496x^71+810x^72+412x^73+654x^74+104x^75+467x^76+24x^77+258x^78+167x^80+4x^81+96x^82+34x^84+14x^86+1x^100

The gray image is a linear code over GF(2) with n=280, k=13 and d=120.
This code was found by Heurico 1.16 in 6.23 seconds.