The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  X  0  X  1  1  1  1  X  0  1  1  X  X  1  1  0  0  1  0  1  X  1  0  1  1  1  1  0  0  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  X X+1 X+1 X+1  1  1  X  0 X+1  1  1 X+1  X  1  1  X  0 X+1  0  X  X  1 X+1  1  X  1  1  X
 0  0  1  0  0  0  0  0  0 X+1  X  1  1  1 X+1 X+1  1 X+1  0  1 X+1  1  0  1 X+1 X+1 X+1  1 X+1  0  X  1  X  1  1  X X+1  0  1 X+1  X
 0  0  0  1  0  0  0  0 X+1  1  X X+1  0  X  X  0  1  1 X+1  0 X+1 X+1  1  0  X  X  0  1  X  1  X  X  0  1  1  0  X  0  X X+1  0
 0  0  0  0  1  0  0  0  1  0  1 X+1  X X+1 X+1 X+1  0  1 X+1  1 X+1  0  X  X  0 X+1  1 X+1 X+1  1 X+1 X+1 X+1  1  1  1  0  0 X+1  1  0
 0  0  0  0  0  1  0  1  0  1 X+1 X+1  X X+1  X X+1  X  0  X  0  1  1  0 X+1  X  0  X  X  0  X X+1 X+1  X  1  1  X X+1  X  0  1  0
 0  0  0  0  0  0  1  1 X+1  X  X  1 X+1  0  0 X+1  0  1  X X+1  0 X+1 X+1  X  0 X+1 X+1  X  0  0  1  1  X  0  X  1 X+1 X+1  0  X  0
 0  0  0  0  0  0  0  X  X  0  0  X  X  0  0  X  0  X  0  X  0  X  X  X  X  0  0  X  X  X  0  0  X  X  X  X  0  0  X  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+44x^29+187x^30+298x^31+482x^32+706x^33+917x^34+1306x^35+1544x^36+1806x^37+2242x^38+2590x^39+2680x^40+2840x^41+2834x^42+2524x^43+2463x^44+2080x^45+1607x^46+1230x^47+855x^48+634x^49+361x^50+218x^51+150x^52+70x^53+44x^54+26x^55+14x^56+12x^57+3x^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 1.16 in 89.2 seconds.