The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+94x^68+64x^69+176x^70+112x^71+33x^72+8x^73+16x^74+4x^75+4x^79

The gray image is a linear code over GF(2) with n=560, k=9 and d=272.
This code was found by Heurico 1.16 in 0.203 seconds.