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  1  1  1  1  1  1  1 X^2  X  0  0  X  0  X  0  1  X  X X^2  1  0  1  X  X  X  X  0 X^2  X  X  X  1
 0  X  0  0  0  0  0  0  0  X X^2+X  X  X X^2+X  X X^2  X X^2 X^2+X X^2  0 X^2  0  X X^2+X  X X^2 X^2+X  0  X  X  X X^2 X^2+X  0  0 X^2+X X^2  0  X X^2+X  X  0 X^2+X X^2  0  0  X X^2+X X^2  X  X  X X^2  X X^2+X  0  0 X^2  X  X X^2  X  0
 0  0  X  0  0  0  X X^2+X  X  0  0  0  X  X X^2+X X^2  X X^2+X X^2  X X^2+X X^2 X^2 X^2  X  0 X^2+X  0 X^2  0 X^2  X  X  X  X  X  X  X X^2  X  0 X^2 X^2  X  X  X  X X^2+X X^2 X^2  0 X^2 X^2+X X^2+X  X  0 X^2+X X^2 X^2 X^2 X^2+X X^2+X  0  0
 0  0  0  X  0  X  X X^2+X  0  X  X X^2  0 X^2 X^2+X  X X^2+X X^2+X X^2+X  0  X  X X^2  0  X  0 X^2 X^2+X X^2 X^2+X X^2 X^2+X X^2+X  0 X^2+X  0 X^2+X X^2+X X^2  0 X^2 X^2  X X^2+X X^2+X X^2 X^2+X  X  0 X^2+X  0  X X^2+X  0  0  0 X^2  0  0 X^2+X X^2+X  0  X  0
 0  0  0  0  X  X  0 X^2+X  X X^2 X^2+X X^2+X  0 X^2+X  X X^2  0  X X^2  X  0  X X^2+X X^2+X  X X^2 X^2  X  0 X^2 X^2  X  X  0 X^2  X  0  X X^2 X^2 X^2 X^2 X^2  0 X^2+X X^2 X^2+X  X X^2+X X^2 X^2+X X^2 X^2  0 X^2  X X^2+X X^2+X  X  0  X X^2+X  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 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  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  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+64x^52+62x^53+187x^54+272x^55+368x^56+414x^57+553x^58+736x^59+834x^60+1178x^61+1361x^62+1538x^63+1519x^64+1356x^65+1280x^66+1158x^67+902x^68+712x^69+529x^70+426x^71+330x^72+220x^73+147x^74+82x^75+69x^76+24x^77+33x^78+12x^79+6x^80+2x^81+4x^82+2x^84+2x^86+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 19.6 seconds.