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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+62x^60+120x^62+32x^63+114x^64+96x^65+212x^66+96x^67+88x^68+32x^69+96x^70+44x^72+20x^74+9x^76+1x^80+1x^124

The gray image is a linear code over GF(2) with n=264, k=10 and d=120.
This code was found by Heurico 1.16 in 0.242 seconds.