The generator matrix

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

generates a code of length 70 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+92x^63+201x^64+276x^65+305x^66+336x^67+414x^68+396x^69+333x^70+320x^71+307x^72+294x^73+268x^74+202x^75+140x^76+72x^77+44x^78+30x^79+16x^80+6x^81+6x^82+8x^83+6x^84+8x^85+2x^86+2x^87+3x^88+4x^89+1x^90+2x^91+1x^94

The gray image is a linear code over GF(2) with n=280, k=12 and d=126.
This code was found by Heurico 1.16 in 1.83 seconds.