The generator matrix

1 0 0 0 0 0 0 1 1 1 X 1 1 0 1 1 0 X X 1 X 0 0 1 1 1 X 1 0 X 0 1 1 0 X 0 X 1 1 1 0 1 0 1 1 1 1 X 1 0 0 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 0 X X X 1 1 1 1 1 1 1 X+1 1 1 1 1 X+1 1 0 X X+1 1 0 1 X 1 1 X+1 1 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 X 0 0 X 1 1 1 1 1 1 1 1 1 0 X X+1 1 X X+1 X+1 X+1 X 0 X 0 X X+1 1 0 X+1 X X+1 1 X 1 0 X 1 0
0 0 0 1 0 0 0 0 0 X X 1 1 1 1 X+1 1 X X X X+1 X+1 X+1 0 X+1 0 1 0 0 0 X X X+1 1 1 X X 0 0 X+1 1 X 0 1 0 1 0 X+1 1 X+1 0 0
0 0 0 0 1 0 0 1 X 1 1 0 X+1 1 0 1 0 X 0 0 0 1 1 X+1 0 X 0 X+1 1 X+1 X+1 X+1 X 0 1 X X+1 X 0 0 X 0 X X 1 1 1 X+1 X+1 1 X+1 0
0 0 0 0 0 1 0 1 X+1 0 1 X X+1 1 1 0 1 X X+1 1 X X+1 X 1 0 0 1 X+1 1 X+1 1 0 0 X+1 1 0 0 0 1 X+1 X+1 1 X 1 X X X+1 X X X 1 0
0 0 0 0 0 0 1 X 1 1 X+1 1 X+1 0 0 X X+1 1 X+1 X 1 1 0 X+1 0 X+1 X X+1 X+1 X 0 1 1 X+1 X+1 X X+1 X+1 X 1 1 X+1 X 1 0 0 0 0 X+1 0 X 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+73x^40+112x^41+290x^42+376x^43+514x^44+582x^45+708x^46+778x^47+902x^48+996x^49+972x^50+1206x^51+1123x^52+1264x^53+1190x^54+1056x^55+938x^56+878x^57+695x^58+484x^59+437x^60+296x^61+199x^62+126x^63+98x^64+30x^65+38x^66+6x^67+10x^68+2x^69+3x^70+1x^82

The gray image is a linear code over GF(2) with n=104, k=14 and d=40.
This code was found by Heurico 1.10 in 8.5 seconds.