The generator matrix

 1  0  0  1  1  1  0 X^3  0 X^2  1  1  1  1 X^3+X  1 X^3+X  1  1  1 X^3+X^2+X X^2+X X^3+X^2+X  1  X  1  1  1  1  1  1  1  0  1  X  1 X^3+X^2 X^3  1 X^3+X^2+X X^3+X^2 X^3+X  1 X^2 X^3  1 X^3+X^2 X^3+X  1  1  1  1  1 X^3+X^2 X^3+X^2+X  1  1 X^3+X X^2+X  1 X^3  1  X  1  1 X^3+X  0  1  1  1
 0  1  0  0 X^2+1 X^3+X^2+1  1 X^2+X  1  1 X^3  0 X^3+1 X^3+1 X^3+X^2+X  X  1  X X+1 X^2+X+1  1 X^2  1 X^3+X^2+X+1  1 X^3+X^2+X+1 X^2+X X^2 X^3+X  0  1 X^3+1 X^3+X^2  1  1 X^3  1  1 X^2  1 X^3+X  1 X^3+X+1  1  1 X^3+X^2+X+1  1 X^3+X X^3+X X^2 X+1 X^3+X^2+X X^2+X  1  1 X^2+X X^2 X^2  1 X^2 X^3 X^3+X^2+X  1 X+1 X^3 X^2+X X^3+X  0 X^3+X+1  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1 X^3+X^2+X  1 X^2+X X^2+1  X X^2+1  1 X^2+X+1 X^3+X X^3+X X^3 X^3+X+1 X^3+X^2+1  1 X^3  X X^3+X+1 X^3+X^2+1 X^3+1 X^3 X^3+X^2  1 X^3 X^3+X^2+1  1 X^3+X^2+X X+1 X^2+X X^3+X+1 X^3 X^3+X^2+X+1 X^2+1  1 X^3+1 X^3+X+1 X^3  X  1 X^3+X^2+X+1  1 X^3+X X^3+X X^3+X^2 X^3+X+1 X^3+X^2  X X^3+X^2+X X^3+1 X^3+X^2  1 X^3+X^2 X^3+X^2+X  1 X^3+1 X^2+1 X+1  1  1  1 X^3+X X^3+X^2+1  0
 0  0  0 X^2 X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3 X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3 X^3  0  0 X^3 X^3 X^3+X^2 X^3 X^2 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^3+X^2  0  0  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+96x^64+702x^65+1166x^66+1624x^67+1770x^68+2048x^69+2035x^70+2134x^71+1608x^72+1326x^73+779x^74+528x^75+214x^76+164x^77+99x^78+30x^79+23x^80+12x^81+15x^82+4x^85+2x^86+4x^87

The gray image is a linear code over GF(2) with n=560, k=14 and d=256.
This code was found by Heurico 1.16 in 4.06 seconds.