The generator matrix

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

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+48x^29+199x^30+300x^31+478x^32+714x^33+943x^34+1216x^35+1575x^36+1820x^37+2193x^38+2498x^39+2670x^40+2930x^41+2875x^42+2730x^43+2406x^44+2056x^45+1539x^46+1184x^47+887x^48+542x^49+373x^50+244x^51+163x^52+76x^53+67x^54+18x^55+12x^56+6x^57+1x^58+2x^59+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 65.2 seconds.