The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+86x^40+26x^42+267x^44+226x^46+576x^48+516x^50+738x^52+516x^54+540x^56+226x^58+252x^60+26x^62+71x^64+22x^68+6x^72+1x^76

The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 2.13 seconds.