The generator matrix
1 0 0 0 1 1 1 1 0 1 1 1 X X X 1 1 1 1 1 1 1 1 X 0 1 1 X 1 0 X 1 0 X 1 0 X 1 X X 1 0 1 1 X 1 1 X X X X 1 X X 1 1 1 1 1 1 1 1
0 1 0 0 1 0 0 1 1 0 1 1 1 1 0 0 X+1 X X+1 X 1 1 0 1 0 X+1 1 0 0 1 1 1 1 1 1 1 1 X 1 1 X+1 0 X 1 1 X 1 1 0 1 1 X+1 1 0 0 0 0 0 0 0 0 0
0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 0 1 X+1 1 1 0 0 X+1 X 1 X 1 1 1 X+1 X+1 X X X X+1 X X+1 X 1 X+1 1 1 X+1 X+1 1 X 1 1 1 1 0 X 0 0 0 0 0 0 0 0 0
0 0 0 1 1 1 0 0 1 1 0 1 1 0 1 X 0 0 0 0 X 0 X 1 1 X+1 X+1 1 X+1 1 1 X X+1 1 0 0 X 1 X+1 0 1 1 0 X 0 0 1 X+1 X+1 1 X 1 1 X 0 0 0 0 0 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 X X 0 X 0 0 0 X 0 0 X 0 X 0 X X X 0 X X 0 0 X X X X 0 X X 0 X X X 0 0 X 0 0 0 X X X 0 0 0 0 0 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 0 X X X 0 0 X 0 0 X 0 X 0 X X 0 0 X X X 0 X X 0 0 X 0 X X X X X X 0 0 X 0 X X 0 0 X 0 0 0 0 0 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 X X X X 0 X 0 0 X X X 0 0 0 0 X 0 0 X X X X 0 0 0 X X X X 0 X 0 0 0 X 0 X X X 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 X X 0 X X X 0 X X X X X 0 X 0 0 0 X 0 0 0 X X X X X 0 X X 0 X X X 0 X 0 0 X X X 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 X 0 X X 0 0 0 X 0 0 X X 0 X X 0 X X X X 0 0 0 0 0 0 0 X 0 X X X X 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X 0 X 0 0 X 0 0 X X X X 0 X 0 0 0 X X X X X 0 X X X 0 0 0 0 X X 0 0 X X 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 X X X X 0 0 0 X 0 0 0 X 0 0 X X X 0 X 0 0 0 X 0 X 0 X X X X 0 0 0 0 X X 0 X 0 0 0 X 0 X 0 0 0 0 0 0 0 0
generates a code of length 62 over Z2[X]/(X^2) who´s minimum homogenous weight is 40.
Homogenous weight enumerator: w(x)=1x^0+80x^40+164x^42+311x^44+488x^46+826x^48+1273x^50+1635x^52+1912x^54+2345x^56+2742x^58+3032x^60+3201x^62+3005x^64+2626x^66+2324x^68+2060x^70+1690x^72+1240x^74+795x^76+494x^78+268x^80+141x^82+61x^84+36x^86+9x^88+6x^90+2x^92+1x^94
The gray image is a linear code over GF(2) with n=124, k=15 and d=40.
This code was found by Heurico 1.16 in 99.3 seconds.