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

generates a code of length 65 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+36x^53+122x^54+140x^55+292x^56+332x^57+441x^58+514x^59+685x^60+918x^61+1120x^62+1374x^63+1458x^64+1560x^65+1418x^66+1382x^67+1146x^68+928x^69+732x^70+560x^71+394x^72+268x^73+197x^74+102x^75+105x^76+54x^77+56x^78+22x^79+15x^80+5x^82+2x^83+2x^86+2x^90+1x^98

The gray image is a linear code over GF(2) with n=260, k=14 and d=106.
This code was found by Heurico 1.16 in 20.3 seconds.