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  X  1  1  1  0  0  X X^2  X  X  0  1  1  0 X^2  X  1 X^2  1  X  1  1  1  1 X^2  1  1  1  0  X  1  0  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X X^2+X  0 X^2+X  X X^2 X^2+X  0 X^2+X  0  X X^2+X X^2+X  0  0 X^2+X  X X^2  0  0  X  X X^2 X^2 X^2  X X^2+X  X  X X^2  X X^2+X X^2+X  X  0 X^2+X  X  0 X^2+X  0  X X^2 X^2+X  0  0  X  0 X^2+X  X X^2+X X^2  X  0
 0  0  X  0  X  X X^2+X  0  0  0  X X^2  X X^2+X X^2 X^2+X X^2 X^2  0 X^2  X  X X^2 X^2+X X^2  X  X X^2  X X^2+X  0  X  X  X X^2+X X^2  0 X^2 X^2  0 X^2+X  0 X^2+X X^2 X^2  X  0 X^2+X  0 X^2  X  0 X^2+X X^2 X^2  X X^2+X  0  X  0  0 X^2  0  0
 0  0  0  X  X  0 X^2+X  X  0  X  0  X X^2+X X^2+X X^2 X^2  0 X^2 X^2+X  X  0  0 X^2+X X^2+X  X  0  X  0  X  X  0  0 X^2 X^2+X X^2  X  0 X^2  X X^2+X  X X^2  0  X  0  X X^2  0  X X^2+X X^2+X  0 X^2  0 X^2 X^2+X  0 X^2  X X^2 X^2 X^2  0  0
 0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 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 X^2 X^2 X^2  0 X^2  0  0  0 X^2  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 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2  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+49x^52+88x^53+144x^54+232x^55+312x^56+362x^57+538x^58+748x^59+939x^60+1126x^61+1376x^62+1500x^63+1548x^64+1564x^65+1376x^66+1200x^67+930x^68+732x^69+478x^70+344x^71+242x^72+186x^73+138x^74+68x^75+56x^76+38x^77+41x^78+4x^79+17x^80+4x^82+1x^84+1x^92+1x^94

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 20.1 seconds.