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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+161x^52+202x^54+16x^55+663x^56+64x^57+802x^58+272x^59+1355x^60+688x^61+1790x^62+1008x^63+2307x^64+1008x^65+1868x^66+688x^67+1436x^68+272x^69+766x^70+64x^71+524x^72+16x^73+194x^74+156x^76+10x^78+40x^80+11x^84+1x^88+1x^92

The gray image is a linear code over GF(2) with n=256, k=14 and d=104.
This code was found by Heurico 1.16 in 21.1 seconds.