The generator matrix

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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+208x^57+620x^58+884x^59+1450x^60+1652x^61+2192x^62+2130x^63+2996x^64+2762x^65+3009x^66+2884x^67+2873x^68+2334x^69+2277x^70+1460x^71+1351x^72+692x^73+481x^74+266x^75+123x^76+58x^77+27x^78+22x^79+4x^80+6x^81+2x^82+2x^83+2x^84

The gray image is a linear code over GF(2) with n=264, k=15 and d=114.
This code was found by Heurico 1.13 in 13.7 seconds.