The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X X X X X X X X 0 X X X 1 1 1 0 X X 1 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 X X X X X X X 0 X X 0 0 X X 0 0 0 X 0 X X 0 X 0 X 0 X X X 0 X 0 0 X X 0 0 0 0
0 0 X 0 0 0 0 0 0 0 0 0 0 0 X 0 0 0 0 X X X X X X X 0 0 0 X 0 X 0 0 X X X X 0 X 0 X 0 X X X X X X X 0 0 X 0 X 0 0 0 X X 0 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 X 0 0 0 X X X X X X 0 0 0 0 X 0 X X 0 0 X 0 0 X X 0 0 0 X X X X X 0 0 0 0 0 X 0 X X 0 X 0 0 X 0 0 0
0 0 0 0 X 0 0 0 0 0 0 0 0 X 0 X X X X X X 0 X X 0 X X X 0 0 0 X 0 0 0 0 X 0 X 0 X 0 0 X 0 X X X X 0 X 0 0 0 0 X X 0 0 X 0 0 0
0 0 0 0 0 X 0 0 0 0 0 0 X 0 0 X X 0 X X 0 X 0 X 0 X X X X 0 0 0 X X 0 0 X 0 0 0 0 0 X 0 0 0 X X 0 X X X X X X 0 X 0 0 X 0 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 0 X X X X 0 X X 0 X 0 X 0 0 X 0 X 0 X 0 X 0 X 0 X X 0 X 0 0 0 0 X X X 0 X 0 0 X 0 0 0 0 X 0 0 0
0 0 0 0 0 0 0 X 0 0 0 X 0 0 0 0 X X 0 X 0 0 0 X X X 0 0 X 0 X 0 X 0 X 0 X 0 0 X 0 0 X 0 X X X 0 X X 0 0 X X X X 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 X 0 0 X 0 0 0 X 0 0 X 0 X 0 0 X 0 0 0 0 X X X 0 0 X 0 X X X 0 X X X 0 X 0 X 0 X X X X 0 X X 0 X 0 X X X 0 0 0
0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 0 0 X 0 0 X X 0 0 X 0 X X 0 X X X 0 0 X 0 0 X X 0 0 X X X X 0 0 X X 0 0 0 X 0 X 0 0 0 X X 0
0 0 0 0 0 0 0 0 0 0 X X X X X 0 0 X X X X X 0 X 0 X 0 0 0 0 0 0 0 0 0 X 0 X X X X X 0 X X 0 0 0 X 0 X 0 0 0 0 0 X X 0 0 0 0 0
generates a code of length 63 over Z2[X]/(X^2) who´s minimum homogenous weight is 48.
Homogenous weight enumerator: w(x)=1x^0+82x^48+49x^50+2x^51+130x^52+18x^53+118x^54+58x^55+195x^56+150x^57+132x^58+248x^59+166x^60+324x^61+177x^62+420x^63+158x^64+380x^65+165x^66+226x^67+138x^68+138x^69+168x^70+66x^71+97x^72+14x^73+111x^74+4x^75+42x^76+78x^78+11x^80+22x^82+4x^84+2x^86+1x^90+1x^94
The gray image is a linear code over GF(2) with n=126, k=12 and d=48.
This code was found by Heurico 1.16 in 3.83 seconds.