The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  1  0  X  0  1  1  1  0  1  0  1  0  X  1  X  1  0  1  0  1  X  0  1  1  X  1  1  X  X  0  1  1  1  1  1  0  1  1  1  1
 0  1  0  1  0  1  1  0  0  1 X+1  X  1  1  0  X  1 X+1  0 X+1  1  X  0  1  X  1  0  0  1  1 X+1  1  X X+1 X+1  1  0  0  X  1  X  1  X  X  1 X+1  1 X+1  1  X  0
 0  0  1  1  1  0  1  0  1 X+1  X  1  X  1  1  0  1 X+1  1  0  0 X+1  1  1  1  1  0  1  1  0  X X+1  1 X+1  X X+1  X  X  1  0  1  0  0 X+1  0  1  1  X X+1  1  0
 0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  X  X  0  0  0  0  X  X  0  X  0  X  X  X  X  X  0  0  0  0  X  X  X  X  X  X  X  0  X  0  0  X  X  0  0
 0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  X  X  0  0  X  X  X  0  0  0  X  0  X  0  0  0  X  X  X  X  0  0  0  0  0  X  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  0  X  X  X  X  X  0  X  0  X  0  X  0  X  0  0  0  X  X  0  X  X  X  0  X  X  X  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  X  X  X  X  X  0  X  X  0  X  X  X  X  0  0  0  0  0  X  0  0  X  0  X  X  0  0  0  0  0  0  X  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  0  X  X  0  0  0  X  X  X  X  X  X  0  0  X  0  X  X  X  0  0  0  0  0  X  X  0  X  0  0  0  0  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  X  0  X  0  0  X  0  X  0  X  0  0  X  X  X  0  0  X  X  X  X  0  0  0  X  X  0  0  0  X  X  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+29x^40+24x^41+111x^42+124x^43+174x^44+138x^45+214x^46+328x^47+258x^48+228x^49+241x^50+388x^51+259x^52+216x^53+275x^54+316x^55+190x^56+132x^57+145x^58+112x^59+84x^60+30x^61+28x^62+12x^63+25x^64+7x^66+3x^68+3x^70+1x^72

The gray image is a linear code over GF(2) with n=102, k=12 and d=40.
This code was found by Heurico 1.16 in 2.07 seconds.