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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0 X^3
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3 X^3
 0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0
 0  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0

generates a code of length 71 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+7x^66+21x^68+35x^70+896x^71+35x^72+21x^74+7x^76+1x^142

The gray image is a linear code over GF(2) with n=568, k=10 and d=264.
This code was found by Heurico 1.16 in 0.25 seconds.