The generator matrix

 1  0  0  0  0  0  1  1  1  X  1  1  X  1  0  0  1  1  0  X  1  X  1  1  1  1  1  X  0  X  1  1  0  1  0  0  0  X  1  1  1
 0  1  0  0  0  0  0  0  0  1  1 X+1  0 X+1  1  1 X+1  1  1  X  0  1  1  X  X X+1  1  X  0  1  1  0  1 X+1  1  1  0  1 X+1  1  0
 0  0  1  0  0  0  0  0  0  0  1 X+1  1  X  0 X+1 X+1  0  X  1  1 X+1  X  1  X  0  0  1  X X+1 X+1  1  1  X  0  0  X  X  1  1  0
 0  0  0  1  0  0  0  1  1  1  0 X+1 X+1  1  1 X+1  1  0  X X+1  1  0  0  X X+1 X+1  1  1  X X+1  1  X X+1 X+1  0  X  1 X+1  0  0  0
 0  0  0  0  1  0  1  1  0  1  0  1 X+1  X  X X+1  X  X  1  X X+1  0 X+1  X  X  1  1  1  1  1  0 X+1  0  1 X+1  1  1  1  X  X  X
 0  0  0  0  0  1  1  0  1  1  X X+1 X+1  1  1  X  0 X+1  0  X X+1 X+1  X  X  0 X+1  X  0  1 X+1 X+1  1  1 X+1  0  1  1 X+1  X  1  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X  0  X  X  0  X  0  X  X  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  X  X  X  0  0  X  X  0  X  0  X  0  X  X  X  X  X  0  0  0  0  X  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  X  X  0  0  0  0  X  0  X  0  X  X  X  0  X  X  X  X  0  X  X  0  X  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+58x^29+173x^30+278x^31+487x^32+726x^33+946x^34+1310x^35+1527x^36+1838x^37+2160x^38+2454x^39+2845x^40+2798x^41+2823x^42+2700x^43+2324x^44+2106x^45+1643x^46+1182x^47+874x^48+582x^49+404x^50+242x^51+115x^52+78x^53+38x^54+22x^55+17x^56+6x^57+3x^58+4x^59+2x^60+2x^62

The gray image is a linear code over GF(2) with n=82, k=15 and d=29.
This code was found by Heurico 1.16 in 66.5 seconds.