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

generates a code of length 69 over Z2[X]/(X^4) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+13x^66+48x^67+114x^68+672x^69+113x^70+48x^71+13x^72+1x^74+1x^134

The gray image is a linear code over GF(2) with n=552, k=10 and d=264.
This code was found by Heurico 1.16 in 17.9 seconds.