The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 0 1 1 0 1 1 X X X 1 1 1 X 0 0 0 X 0 X 1 0 1 1 1 X 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 X 1 0 0 X 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X 1 1 X+1 1 1 1 1 1 1 1 1 X+1 0 1 1 1 1 1 X X+1 X X X 0 1 0 0 X+1 X 1 1 0 0 1 X X+1 X 1 X 1 1 0 X+1 0 1 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 0 0 X X X X 0 X 0 X 0 X 1 X+1 X+1 1 1 1 1 X+1 1 1 1 1 1 1 X+1 1 X+1 X+1 X+1 1 0 X 1 1 X X+1 1 X+1 1 1 X 0 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 1 X 0 X 0 1 X+1 1 X X+1 X 1 1 1 0 1 X+1 X X X+1 1 0 0 X+1 X 1 X+1 X+1 X+1 0 X+1 1 0 X X+1 X X X X X X+1 0 0 0 0 0 X 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 1 X X 0 X+1 X+1 X+1 X 1 X+1 1 0 X+1 1 1 X+1 0 1 1 X X X X+1 0 X+1 X+1 1 1 X 0 X X+1 X 1 1 X 0 1 1 X 1 0 0 1 1 X 1 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X 1 0 X+1 X X 1 X 1 X+1 X+1 X+1 0 X+1 0 X+1 1 1 X X X+1 X 1 1 0 1 X 1 0 X+1 0 X 1 X X 0 X X 0 0 0 0 0 X+1 X 1 X 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 0 0 X+1 X+1 0 X+1 X+1 1 X X X+1 1 X+1 1 X+1 X 1 X+1 1 1 0 X+1 1 X+1 X 0 0 X+1 X X+1 1 1 X+1 X 0 0 1 0 X 0 1 X+1 X+1 0 X 0 X+1 0

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+85x^52+106x^53+247x^54+314x^55+460x^56+554x^57+637x^58+726x^59+770x^60+842x^61+907x^62+1090x^63+966x^64+1042x^65+1019x^66+942x^67+907x^68+948x^69+823x^70+688x^71+640x^72+468x^73+360x^74+292x^75+242x^76+128x^77+95x^78+44x^79+21x^80+8x^81+7x^82+4x^84+1x^106

The gray image is a linear code over GF(2) with n=130, k=14 and d=52.
This code was found by Heurico 1.10 in 11.5 seconds.