The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+76x^57+182x^58+280x^59+297x^60+334x^61+397x^62+338x^63+379x^64+424x^65+368x^66+294x^67+230x^68+168x^69+122x^70+88x^71+35x^72+14x^73+13x^74+22x^75+12x^76+6x^77+4x^78+2x^79+5x^80+2x^81+1x^82+1x^84+1x^86

The gray image is a linear code over GF(2) with n=256, k=12 and d=114.
This code was found by Heurico 1.16 in 1.01 seconds.