The generator matrix

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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+156x^56+136x^57+796x^58+588x^59+1585x^60+1200x^61+2394x^62+1756x^63+3357x^64+2372x^65+3908x^66+2452x^67+3552x^68+2020x^69+2380x^70+1108x^71+1392x^72+516x^73+598x^74+112x^75+221x^76+28x^77+88x^78+38x^80+10x^82+2x^84+2x^86

The gray image is a linear code over GF(2) with n=264, k=15 and d=112.
This code was found by Heurico 1.16 in 46.7 seconds.