The generator matrix

 1  0  1  1  1  0  1  1  0  1  1  X  1  1  0  1  0  1  1  0  0  1  1  0  1  1  1  1  1  0  1  X  0  1  1  0  1  1  1  0  1  1  X  1  1  X  1  0  1  X  1
 0  1  1  0  1  1  0  1  1  0 X+1  1  X X+1  1  0  1 X+1 X+1  1  1  0  X  1  0 X+1 X+1 X+1  0  1 X+1  1  1  0  0  1  0  X  X  1 X+1 X+1  1  1  X  1  0  1 X+1  0  0
 0  0  X  0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  0  X  0  X  X  X  0  X  0  0  0  0  X  0  X  X  X  0  X  X  X  0  0  X  0  0  0  X  0
 0  0  0  X  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X  0  X  0  X  0  X  0  0  0  X  X  0  X  X  0  0  0  X  X  X  0  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  X  0  X  X  0  0  X  0  X  0  0  X  0  0  0  X  X  X  X  0  0  X  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  0  X  X  0  X  0  0  X  0  0  X  X  X  0  X  0  0  0  0  X  X  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  X  X  X  0  0  0  X  X  0  X  0  X  0  0  X  0  X  X  0  0  X  X  X  X  0  X  0  0  X  X  X  0  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  0  X  X  X  X  0  X  0  X  0  0  0  X  0  X  0  0  X  X  0  0  X  X  X  0  0  X  0  0  0  X  X  0  0  0  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  X  0  0  0  0  0  X  X  0  X  0  0  X  0  0  X  X  X  0  X  0  0  0  0  0  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  0  X  X  0  X  0  X  0  X  X  0  X  X  X  X  0  0  0  0  0  0  X  0  X  0  0  X  0  X  0  0  0  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+91x^40+14x^41+90x^42+72x^43+166x^44+166x^45+188x^46+256x^47+265x^48+332x^49+251x^50+368x^51+234x^52+332x^53+249x^54+256x^55+189x^56+166x^57+144x^58+72x^59+58x^60+14x^61+70x^62+14x^64+27x^66+6x^68+5x^70

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 2.18 seconds.