The generator matrix

 1  0  0  1  1  1 X^2+X  1  X  0 X^2  1  1  1 X^2+X  1  1  0  1 X^2+X  1 X^2  1  1  1 X^2+X X^2+X  1  1  1  1  1 X^2+X X^2  1  X X^2 X^2+X  1 X^2+X  0  1  X  1  1  1  0  1  1 X^2+X X^2  1  1  X X^2  X  1 X^2  0 X^2+X  1  1 X^2  1
 0  1  0  0  1  1  1 X^2  1  0  1 X^2 X+1  1  0 X^2  1  1 X^2+X  1 X^2+X+1  1  0 X^2  1  1 X^2+X X+1  X X^2+1 X^2+X+1 X^2  1  1  X X^2  1  0 X^2  X  1  X  1 X^2+X+1 X^2+X  1  X X^2 X^2+X  1  0  0 X^2+X+1  1  1  1 X^2+1  1  1  1 X^2  X  1 X^2+1
 0  0  1  1  1  0  1 X^2 X^2+1  1 X^2+X X^2+X+1  0  1  1 X^2  X X^2+X+1 X^2+1 X+1 X+1 X^2+X X^2+X+1 X^2+X X^2+1 X^2  1  X X^2 X^2  1 X^2+X+1 X^2+X+1  X X^2  1 X^2+X+1  1 X^2+1  1  1  1  0  0  X X^2+X  1 X^2+X  0 X^2+X  1 X^2+X+1  1 X^2+X+1  X X^2+X  1 X+1  X X^2+X+1  0  0 X^2+1  1
 0  0  0  X  0  0  0  0  0  0  0  X X^2 X^2 X^2+X  X X^2+X  X X^2  X X^2 X^2+X  0 X^2+X  X X^2+X X^2+X X^2+X  X X^2  0  0  X X^2+X X^2  X X^2 X^2+X X^2+X  0  0 X^2+X X^2+X X^2  X  0 X^2+X  X  X X^2 X^2  0 X^2 X^2 X^2+X X^2 X^2  0  0 X^2 X^2+X X^2  0  X
 0  0  0  0  X  0  0  0  0  0  0  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  X  X  X X^2+X  X X^2+X  X X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X X^2+X  X  X  0  X  0 X^2+X X^2 X^2+X  X  0 X^2+X X^2  X  0 X^2+X  X  X X^2
 0  0  0  0  0  X X^2+X X^2+X X^2  X  X  X  0  0  X X^2+X  0 X^2+X X^2+X X^2 X^2+X X^2+X X^2  0 X^2 X^2  0  X  X X^2  X  0 X^2+X  X X^2 X^2+X  0 X^2  0 X^2+X  X  X  X X^2+X  0  0 X^2  X X^2 X^2+X  0  X  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2+X  X 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+158x^54+164x^55+684x^56+612x^57+1384x^58+1196x^59+2273x^60+2300x^61+2898x^62+2872x^63+3542x^64+2996x^65+3288x^66+2188x^67+2219x^68+1256x^69+1100x^70+588x^71+497x^72+128x^73+252x^74+32x^75+84x^76+4x^77+40x^78+12x^80

The gray image is a linear code over GF(2) with n=256, k=15 and d=108.
This code was found by Heurico 1.16 in 45.3 seconds.