The generator matrix

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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+180x^54+500x^55+1199x^56+1638x^57+2517x^58+2974x^59+4190x^60+4614x^61+5787x^62+5690x^63+6710x^64+5622x^65+6339x^66+4688x^67+4275x^68+2982x^69+2367x^70+1378x^71+904x^72+476x^73+268x^74+120x^75+59x^76+28x^77+14x^78+8x^79+6x^80+2x^83

The gray image is a linear code over GF(2) with n=256, k=16 and d=108.
This code was found by Heurico 1.13 in 50.7 seconds.