The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+115x^28+136x^29+525x^30+556x^31+1119x^32+1228x^33+1831x^34+2322x^35+3104x^36+3788x^37+4400x^38+5252x^39+5135x^40+6120x^41+5309x^42+5388x^43+4567x^44+3768x^45+3206x^46+2380x^47+1910x^48+1156x^49+949x^50+466x^51+390x^52+180x^53+156x^54+20x^55+43x^56+8x^57+7x^58+1x^62

The gray image is a linear code over GF(2) with n=82, k=16 and d=28.
This code was found by Heurico 1.11 in 112 seconds.