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

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+149x^60+382x^62+36x^63+522x^64+144x^65+676x^66+320x^67+933x^68+512x^69+962x^70+536x^71+897x^72+336x^73+622x^74+128x^75+483x^76+32x^77+230x^78+4x^79+167x^80+60x^82+43x^84+10x^86+4x^88+2x^90+1x^104

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 6.32 seconds.