The generator matrix

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

generates a code of length 52 over Z2[X]/(X^2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+58x^38+212x^39+375x^40+634x^41+868x^42+1212x^43+1684x^44+1912x^45+2558x^46+3130x^47+3565x^48+4280x^49+4425x^50+4864x^51+5267x^52+5096x^53+4848x^54+4340x^55+3771x^56+3210x^57+2666x^58+2028x^59+1487x^60+1080x^61+730x^62+514x^63+318x^64+148x^65+97x^66+72x^67+41x^68+24x^69+6x^70+12x^71+2x^72+1x^76

The gray image is a linear code over GF(2) with n=104, k=16 and d=38.
This code was found by Heurico 1.11 in 156 seconds.