The generator matrix

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

generates a code of length 66 over Z2[X]/(X^4) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+64x^62+262x^63+360x^64+270x^65+271x^66+242x^67+188x^68+226x^69+109x^70+22x^71+26x^72+2x^74+2x^79+1x^80+1x^82+1x^94

The gray image is a linear code over GF(2) with n=528, k=11 and d=248.
This code was found by Heurico 1.16 in 0.313 seconds.