The generator matrix

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

generates a code of length 41 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+52x^29+171x^30+304x^31+478x^32+664x^33+1014x^34+1252x^35+1517x^36+1818x^37+2341x^38+2578x^39+2527x^40+2922x^41+2841x^42+2620x^43+2356x^44+2052x^45+1637x^46+1192x^47+889x^48+616x^49+392x^50+224x^51+149x^52+62x^53+51x^54+22x^55+17x^56+6x^57+1x^58+2x^60

The gray image is a linear code over GF(2) with n=82, k=15 and d=29.
This code was found by Heurico 1.11 in 26.9 seconds.