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  1  1  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  1  1  1  1  1  1  1  X  1  1  1 X^2 X^2  1  1 X^2  X  X  X
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2 X^3  0  0 X^2 X^3+X^2 X^2  0 X^2 X^3 X^3+X^2  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3  0 X^3 X^3+X^2 X^3+X^2  0 X^3  0  0 X^3+X^2  0 X^3 X^3 X^3  0 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^2  0 X^2 X^3 X^3 X^3 X^2  0
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0 X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^2  0 X^3+X^2  0  0 X^3+X^2 X^3 X^2 X^2  0 X^3 X^3+X^2  0 X^3  0 X^2  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3 X^3+X^2 X^3  0 X^3+X^2  0 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3 X^2 X^3+X^2 X^3 X^2 X^3 X^2  0  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^3 X^3+X^2 X^2  0 X^3+X^2  0 X^2 X^3 X^2 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3  0  0 X^3 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3+X^2 X^3 X^2 X^3 X^2  0 X^2 X^3 X^3+X^2 X^3 X^2 X^3+X^2  0 X^2 X^2 X^3+X^2 X^3 X^3  0 X^2 X^2 X^3+X^2 X^3  0 X^2 X^3 X^3+X^2 X^3 X^3+X^2 X^3
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  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+71x^64+4x^65+118x^66+48x^67+211x^68+328x^69+496x^70+336x^71+239x^72+52x^73+58x^74+44x^76+28x^78+9x^80+4x^82+1x^124

The gray image is a linear code over GF(2) with n=560, k=11 and d=256.
This code was found by Heurico 1.16 in 0.453 seconds.