The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+196x^62+108x^63+444x^64+332x^65+790x^66+468x^67+809x^68+628x^69+842x^70+628x^71+759x^72+468x^73+662x^74+332x^75+315x^76+108x^77+128x^78+105x^80+32x^82+26x^84+6x^86+2x^88+2x^92+1x^96

The gray image is a linear code over GF(2) with n=280, k=13 and d=124.
This code was found by Heurico 1.16 in 21.8 seconds.