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

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+20x^69+66x^70+86x^71+55x^72+18x^73+5x^74+2x^75+2x^85+1x^106

The gray image is a linear code over GF(2) with n=568, k=8 and d=276.
This code was found by Heurico 1.16 in 0.25 seconds.