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

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+78x^70+9x^72+8x^73+2x^74+5x^76+1x^84

The gray image is a linear code over GF(2) with n=560, k=7 and d=276.
This code was found by Heurico 1.16 in 0.313 seconds.