The generator matrix

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

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+248x^55+534x^56+832x^57+1393x^58+1488x^59+2213x^60+2362x^61+2946x^62+2818x^63+3297x^64+2724x^65+2986x^66+2290x^67+2304x^68+1568x^69+1102x^70+754x^71+434x^72+204x^73+129x^74+46x^75+47x^76+22x^77+20x^78+4x^79+2x^80

The gray image is a linear code over GF(2) with n=256, k=15 and d=110.
This code was found by Heurico 1.16 in 43 seconds.