The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+162x^54+520x^56+666x^58+889x^60+889x^62+1004x^64+1019x^66+908x^68+860x^70+577x^72+398x^74+171x^76+95x^78+25x^80+5x^82+2x^86+1x^88

The gray image is a linear code over GF(2) with n=130, k=13 and d=54.
This code was found by Heurico 1.16 in 10 seconds.