The generator matrix
1 0 0 1 1 1 0 1 1 1 1 1 0 X 0 1 1 1 0 1 0 1 0 X 1 X 1 0 1 0 1 X 0 1 1 X 1 1 X X 0 1 1 1 1 1 0 1 1 1 1
0 1 0 1 0 1 1 0 0 1 X+1 X 1 1 0 X 1 X+1 0 X+1 1 X 0 1 X 1 0 0 1 1 X+1 1 X X+1 X+1 1 0 0 X 1 X 1 X X 1 X+1 1 X+1 1 X 0
0 0 1 1 1 0 1 0 1 X+1 X 1 X 1 1 0 1 X+1 1 0 0 X+1 1 1 1 1 0 1 1 0 X X+1 1 X+1 X X+1 X X 1 0 1 0 0 X+1 0 1 1 X X+1 1 0
0 0 0 X 0 0 0 0 0 X 0 0 0 0 0 0 X X 0 0 0 0 X X 0 X 0 X X X X X 0 0 0 0 X X X X X X X 0 X 0 0 X X 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X X X X 0 0 0 X X X 0 0 X X X 0 0 0 X 0 X 0 0 0 X X X X 0 0 0 0 0 X X 0 0 0
0 0 0 0 0 X 0 0 0 0 X 0 0 0 0 0 0 0 0 X X 0 X X X X X 0 X 0 X 0 X 0 X 0 0 0 X X 0 X X X 0 X X X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X X X X X 0 X X 0 X X X X 0 0 0 0 0 X 0 0 X 0 X X 0 0 0 0 0 0 X X 0
0 0 0 0 0 0 0 X 0 X X X 0 0 X 0 X 0 X X 0 0 0 X X X X X X 0 0 X 0 X X X 0 0 0 0 0 X X 0 X 0 0 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X X X X X 0 X 0 0 X 0 X 0 X 0 0 X X X 0 0 X X X X 0 0 0 X X 0 0 0 X X X 0 X X 0
generates a code of length 51 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+29x^40+24x^41+111x^42+124x^43+174x^44+138x^45+214x^46+328x^47+258x^48+228x^49+241x^50+388x^51+259x^52+216x^53+275x^54+316x^55+190x^56+132x^57+145x^58+112x^59+84x^60+30x^61+28x^62+12x^63+25x^64+7x^66+3x^68+3x^70+1x^72
The gray image is a linear code over GF(2) with n=102, k=12 and d=40.
This code was found by Heurico 1.16 in 2.07 seconds.