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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+174x^55+538x^56+920x^57+1366x^58+1592x^59+2262x^60+2380x^61+2696x^62+2896x^63+3156x^64+2894x^65+2911x^66+2442x^67+2138x^68+1576x^69+1200x^70+678x^71+459x^72+220x^73+145x^74+74x^75+18x^76+20x^77+2x^78+4x^80+6x^81

The gray image is a linear code over GF(2) with n=256, k=15 and d=110.
This code was found by Heurico 1.13 in 13.3 seconds.