The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^3+X^2+X X^2  1  1  1  1  1  1 X^3+X^2+X X^3+X^2  1  1  1  1 X^2  1 X^3+X^2+X  1  1 X^3  1  1  1  1  1  1  1  1  1  0  1  1  0  X X^3+X  1  X X^2  1  1  1  X  1  1  1  1  1  1  1  1  1  0  1 X^2+X  1  1  1
 0  1  1 X^2 X+1  1  X X^3+1  1 X^2+X X^3+X+1  1  1  1  0 X^3+X^2+X+1 X^3+X X^3+1 X^3+X^2+X X^3+X^2+X+1  1  1 X^3+X^2 X^3+X^2+1 X^3+X X^3+X+1  1 X^3+X^2+1  1 X^2+X X^3  1 X^2+X+1 X^3+X^2 X^3+X^2+X+1 X^2+X X^2+1 X^3+X  0 X^3+X^2 X^3+X+1  1 X^3+X^2+1 X^3+1  1  1  1 X^3+X^2+1 X^3  1  0  0 X^3+X  0 X^2 X^3+X^2+X X^3+X^2 X^3 X^2+X X^3+X^2+X X^2 X^2+X X^2  X  X  1 X^3+X^2+X X^3+X X^3+X^2+X
 0  0  X X^3+X X^3 X^3+X X^3+X X^3  0  0  X X^2+X X^3+X^2 X^2 X^3+X^2 X^3+X^2+X X^2 X^2+X X^3+X X^3 X^3+X X^2+X X^2+X X^2 X^2+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2+X  X  X X^2  0  X X^3+X^2 X^3+X^2+X X^3 X^3+X^2+X X^3+X^2 X^2+X X^2+X  X X^3+X^2 X^2 X^2  0 X^3+X^2 X^2+X X^3 X^3+X X^2+X X^3+X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^2 X^2 X^3+X^2  0 X^3+X  X  X X^2+X  X X^3  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+274x^66+428x^67+286x^68+308x^69+156x^70+300x^71+169x^72+28x^73+48x^74+24x^75+16x^76+8x^82+2x^98

The gray image is a linear code over GF(2) with n=552, k=11 and d=264.
This code was found by Heurico 1.16 in 0.234 seconds.