The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  1  1  1 X^2  1 X^2  0  1  1  0 X^2  1  1  1  X  1  1  0 X^2  1 X^2  1  1  1  0  1  X  X
 0  X  0  0  0  X X^2+X  X X^2  0  0 X^2 X^2+X  X X^2+X X^2+X  0 X^2 X^2 X^2 X^2  X  X  X X^2+X  X X^2+X X^2  0  X  X X^2 X^2  0  0 X^2+X X^2 X^2+X  X  X X^2  X  X X^2 X^2+X  0 X^2  X X^2+X X^2+X X^2  0 X^2  X  0 X^2  X X^2+X X^2+X X^2  0 X^2 X^2+X  X
 0  0  X  0  X  X  X  0 X^2 X^2+X  0  X X^2+X X^2+X X^2 X^2  0  0  X X^2+X X^2  X X^2+X  0 X^2 X^2+X X^2  X  X  0  X  0 X^2 X^2  X  X  X X^2+X X^2  X  0 X^2+X X^2+X X^2+X X^2+X  0  X  X X^2  0 X^2+X X^2 X^2+X  0  X X^2 X^2  X X^2  X  X  0  0 X^2
 0  0  0  X  X  0  X X^2+X  0 X^2+X  X X^2  0  X X^2+X  0 X^2 X^2+X X^2 X^2+X X^2+X  0 X^2  X  0  X X^2 X^2 X^2+X  X  X  0 X^2+X  X  X  0  0 X^2 X^2+X X^2 X^2+X  0 X^2+X  X  X  X X^2+X  0  0 X^2 X^2  X X^2 X^2+X X^2+X  X  X X^2 X^2+X  X  0  0  0 X^2+X
 0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  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+64x^57+86x^58+120x^59+162x^60+164x^61+216x^62+180x^63+161x^64+192x^65+208x^66+158x^67+79x^68+72x^69+42x^70+30x^71+34x^72+16x^73+22x^74+18x^75+10x^76+4x^77+2x^78+6x^79+1x^100

The gray image is a linear code over GF(2) with n=256, k=11 and d=114.
This code was found by Heurico 1.16 in 77.3 seconds.