The generator matrix

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

generates a code of length 40 over Z2[X]/(X^2) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+46x^27+143x^28+312x^29+611x^30+844x^31+1278x^32+1840x^33+2339x^34+3078x^35+3731x^36+4598x^37+5309x^38+5570x^39+5624x^40+5640x^41+5608x^42+4802x^43+3901x^44+3206x^45+2477x^46+1704x^47+1027x^48+712x^49+507x^50+314x^51+153x^52+74x^53+43x^54+26x^55+14x^56+2x^58+2x^61

The gray image is a linear code over GF(2) with n=80, k=16 and d=27.
This code was found by Heurico 1.11 in 108 seconds.