The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  1  1  1  X  X  X  1  0  1  0  X  0  1  0  X  X  X  X  X  X  1  0  1  0  1  1  1  X  0  X  1  1  X  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  1 X+1  1  1  1  1 X+1  1 X+1  1  0  1  X  1  1  0  0  X  1  0  X  1  X  1  X  0  X  1  X  1  0  0  1  0
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  0  X  X  X  X  0  X  X  1  1 X+1  1  1  1 X+1  1  1  1 X+1 X+1  1 X+1 X+1  1  X X+1  1 X+1  1  1
 0  0  0  1  0  0  0  0  0  X  X  1  1 X+1 X+1  1  1 X+1 X+1  1 X+1  0 X+1 X+1 X+1  0  0  1  1  1 X+1 X+1  1  X  X  0 X+1  1  0 X+1  X  0  0  1  X  0  X  1  X X+1  X
 0  0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  X X+1  1  X  X  0  1  0  X  0  1  0  X  1  X X+1  0  X X+1  0 X+1  0 X+1  0  X X+1  1  X  X  X  X  1  0 X+1  1
 0  0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  0  X X+1 X+1  X  1  0  1 X+1  0 X+1 X+1 X+1 X+1  X  X  0  0  1 X+1  1  1 X+1  1 X+1  X  1  X X+1  X  0  1 X+1 X+1 X+1 X+1  1
 0  0  0  0  0  0  1  1  X  1  1 X+1  X  1  X  1  X  0  1 X+1 X+1 X+1 X+1  X  0  0  X  1 X+1  X  X  1  1  1  0  1 X+1  1  1  X  X  1 X+1 X+1  0 X+1  X  1  1  1  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+244x^40+710x^42+1209x^44+1534x^46+2073x^48+2344x^50+2482x^52+2160x^54+1644x^56+1058x^58+594x^60+242x^62+69x^64+16x^66+2x^68+1x^76+1x^80

The gray image is a linear code over GF(2) with n=102, k=14 and d=40.
This code was found by Heurico 1.16 in 51.6 seconds.