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  X  0  X  1  X X^2  X  1  0  1  X  X  1  0  1  0  1  1  X  X  1  1  0  1  X  0  1  X  1  1  1  X  1 X^2  1  X  X  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 X^2 X^2 X^2+X  X  X  X  X  0 X^2  0 X^2+X  X X^2 X^2  X  X  0  X  0  X X^2+X X^2  0  X  X  X  0  0 X^2+X  X X^2  0  X X^2+X  0  0 X^2  X X^2+X  X  X  X X^2  X  0 X^2 X^2+X  0  0
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X  0 X^2  X  0  X X^2 X^2+X X^2+X  0 X^2+X X^2  0  0  X  X  X  X X^2+X X^2+X  X  X X^2  X  0 X^2  0  0 X^2+X  X  0  X  0 X^2+X  X X^2+X X^2+X  X X^2  X  X X^2+X X^2  X  X  X  X  X  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  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  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 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  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2 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 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 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 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0
 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  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0  0 X^2  0  0 X^2  0 X^2 X^2 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+64x^52+52x^53+129x^54+132x^55+224x^56+350x^57+311x^58+736x^59+389x^60+1338x^61+444x^62+2190x^63+481x^64+2606x^65+478x^66+2264x^67+510x^68+1440x^69+397x^70+680x^71+259x^72+322x^73+219x^74+120x^75+89x^76+34x^77+50x^78+22x^79+24x^80+2x^81+16x^82+4x^84+4x^86+3x^88

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 20.6 seconds.