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

generates a code of length 67 over Z2[X]/(X^4) who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+26x^65+206x^66+556x^67+207x^68+26x^69+1x^70+1x^130

The gray image is a linear code over GF(2) with n=536, k=10 and d=260.
This code was found by Heurico 1.16 in 9 seconds.