The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+49x^66+354x^67+339x^68+194x^69+232x^70+176x^71+303x^72+310x^73+61x^74+6x^75+4x^76+12x^77+4x^79+1x^90+1x^94+1x^96

The gray image is a linear code over GF(2) with n=560, k=11 and d=264.
This code was found by Heurico 1.16 in 1.14 seconds.