The generator matrix
1 0 0 0 1 1 1 0 1 1 1 1 X X X X 0 1 X 1 1 X X X 1 1 1 1 1 X 1 1 1 X 1 X X X 1 1 0 1
0 1 0 0 0 1 1 1 0 0 1 X+1 1 0 1 1 X X 1 X+1 X+1 X X 1 X 0 X 0 X+1 1 X+1 X X+1 1 1 0 X 1 X+1 X+1 1 1
0 0 1 0 1 1 0 1 0 1 1 0 0 1 1 X 1 0 1 X+1 1 0 1 X+1 X+1 1 X 1 X 1 0 0 X+1 X 0 X 1 1 0 0 X 1
0 0 0 1 1 0 1 1 1 0 1 0 1 1 0 X X 1 0 X 1 1 X+1 X+1 X X+1 0 1 0 1 X+1 X+1 X+1 1 1 1 X+1 X+1 0 X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 0 0 X X 0 0 X X X X X X 0 X X 0 X 0 0 X X X 0 0 X X 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X X 0 0 X 0 X 0 X 0 X X 0 X 0 0 X X 0 X X X X X X X
0 0 0 0 0 0 X 0 0 0 0 X 0 0 X X 0 X X 0 X 0 0 X X 0 X 0 0 0 X X X 0 X 0 0 X X 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 X X 0 X X X 0 X 0 X 0 X 0 X 0 X X 0 0 0 X X X 0 X 0 X 0
0 0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 0 X X X 0 X X X X 0 X 0 X 0 0 X X X 0 X 0 X 0 0 0
0 0 0 0 0 0 0 0 0 X 0 0 X 0 X X 0 X X X 0 X 0 0 0 0 X 0 X X 0 0 0 X X 0 0 X X 0 0 X
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 X X X 0 X X X X 0 0 X X 0 0 0 0 0 X 0 0 0 0 0 X X X
generates a code of length 42 over Z2[X]/(X^2) who´s minimum homogenous weight is 29.
Homogenous weight enumerator: w(x)=1x^0+32x^29+129x^30+166x^31+356x^32+404x^33+638x^34+930x^35+1211x^36+1468x^37+1881x^38+2308x^39+2484x^40+2880x^41+2887x^42+2836x^43+2589x^44+2344x^45+1925x^46+1566x^47+1254x^48+868x^49+593x^50+362x^51+261x^52+188x^53+127x^54+24x^55+32x^56+8x^57+9x^58+3x^60+2x^62+1x^64+1x^66
The gray image is a linear code over GF(2) with n=84, k=15 and d=29.
This code was found by Heurico 1.16 in 80.6 seconds.