The generator matrix

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

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+58x^40+80x^41+207x^42+290x^43+339x^44+366x^45+397x^46+470x^47+481x^48+528x^49+585x^50+590x^51+540x^52+610x^53+490x^54+486x^55+452x^56+358x^57+289x^58+168x^59+155x^60+104x^61+70x^62+44x^63+16x^64+2x^65+7x^66+6x^68+2x^70+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 6.9 seconds.