The generator matrix

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

generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+25x^56+16x^57+64x^58+78x^59+59x^60+72x^61+66x^62+60x^63+68x^64+64x^65+51x^66+64x^67+55x^68+72x^69+44x^70+52x^71+26x^72+32x^73+17x^74+2x^75+11x^76+8x^78+7x^80+3x^82+3x^84+2x^86+1x^88+1x^90

The gray image is a linear code over GF(2) with n=130, k=10 and d=56.
This code was found by Heurico 1.16 in 0.212 seconds.