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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+160x^52+72x^54+4x^55+545x^56+88x^57+412x^58+372x^59+956x^60+928x^61+812x^62+1672x^63+1205x^64+2064x^65+936x^66+1672x^67+1199x^68+928x^69+624x^70+372x^71+676x^72+88x^73+188x^74+4x^75+279x^76+28x^78+66x^80+29x^84+3x^88+1x^92

The gray image is a linear code over GF(2) with n=260, k=14 and d=104.
This code was found by Heurico 1.16 in 23.8 seconds.