The generator matrix

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

generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+34x^40+100x^41+194x^42+278x^43+320x^44+334x^45+432x^46+456x^47+488x^48+606x^49+551x^50+574x^51+616x^52+548x^53+546x^54+504x^55+414x^56+376x^57+268x^58+202x^59+148x^60+78x^61+45x^62+32x^63+23x^64+6x^65+11x^66+2x^67+4x^68+1x^78

The gray image is a linear code over GF(2) with n=102, k=13 and d=40.
This code was found by Heurico 1.16 in 6.94 seconds.