The generator matrix

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

generates a code of length 70 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+24x^69+196x^70+24x^71+1x^72+4x^74+1x^76+4x^78+1x^84

The gray image is a linear code over GF(2) with n=560, k=8 and d=276.
This code was found by Heurico 1.16 in 0.11 seconds.