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

generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+80x^51+159x^52+234x^53+298x^54+322x^55+389x^56+436x^57+492x^58+510x^59+535x^60+496x^61+431x^62+506x^63+493x^64+456x^65+492x^66+416x^67+371x^68+322x^69+197x^70+178x^71+147x^72+100x^73+64x^74+34x^75+15x^76+4x^77+9x^78+2x^79+2x^80+1x^86

The gray image is a linear code over GF(2) with n=124, k=13 and d=51.
This code was found by Heurico 1.16 in 9.17 seconds.