The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  X  1  1  X  X  1  X  X  X  0  X  1  1  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  X  X  X  0  X  0  X  0  X  X  X  X  0  X  0  X  0  0  0  0  X  0  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  X  X  0  X  0  0  0  X  0  0  X  X  0  0  X  X  0  X  0  X  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  X  X  0  X  X  X  0  X  0  0  X  X  X  X  X  X  0  0  0  0  0  X  X  X  0  0  0  X  X  X  0  X
 0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  X  X  X  0  0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  0  X  0  X  X  X  0  0  X  0  X  X
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  X  0  0  X  0  0  X  X  0  0  0  X  X  0  0  0  X  0  X  X  0  0  0  X  0  0  0  X  0  X  X  0  X
 0  0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  0  X  0  0  X  X  0  X  0  X  0  X  0  X  0  X  X  X  X  X  0  X  X  0  0  0  X  X  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  0  0  X  0  X  X  0  0  X  X  X  0  0  X  X  0  X  X  0  X  0  0  0  X  X  0  0  0  X  0  X  0  X  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  0  0  X  X  X  X  0  0  0  X  0  X  0  0  X  0  X  0  X  X  X  0  0  X  0  X  0  0  X  0  0
 0  0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  X  X  0  X  0  X  0  X  0  X  X  0  0  X  X  X  X  0  X  X  X  X  X  X  X  X  0  0  X  0  X  0  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+97x^40+10x^42+229x^44+90x^46+351x^48+212x^50+402x^52+164x^54+263x^56+34x^58+126x^60+2x^62+56x^64+10x^68+1x^76

The gray image is a linear code over GF(2) with n=102, k=11 and d=40.
This code was found by Heurico 1.16 in 0.681 seconds.