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

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+74x^63+129x^64+110x^65+98x^66+168x^67+214x^68+196x^69+200x^70+180x^71+188x^72+130x^73+76x^74+60x^75+64x^76+58x^77+8x^78+26x^79+33x^80+16x^81+2x^82+4x^83+10x^84+2x^85+1x^112

The gray image is a linear code over GF(2) with n=280, k=11 and d=126.
This code was found by Heurico 1.16 in 89.3 seconds.