The generator matrix

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

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+75x^62+194x^63+371x^64+550x^65+573x^66+682x^67+784x^68+724x^69+761x^70+722x^71+541x^72+530x^73+480x^74+346x^75+279x^76+216x^77+163x^78+94x^79+33x^80+20x^81+27x^82+8x^83+5x^84+8x^85+1x^86+2x^87+2x^88

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 3.49 seconds.