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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+322x^63+378x^64+300x^65+257x^66+220x^67+222x^68+194x^69+55x^70+62x^71+13x^72+14x^73+4x^75+4x^79+1x^88+1x^92

The gray image is a linear code over GF(2) with n=528, k=11 and d=252.
This code was found by Heurico 1.16 in 0.281 seconds.