The generator matrix
1 0 0 0 0 1 1 1 0 1 1 X 1 0 1 0 0 1 X 1 1 X 0 X 1 1 X 1 X 1 1 0 1 X 1 1 X X 1 1 1 X X 1 1 0 1 0 X 1 X 1 1 1 0 X 1 1 1 0 0 1 1 0 0 1
0 1 0 0 0 0 0 0 0 1 1 1 1 1 X+1 X 1 1 1 1 X 0 1 0 X 0 1 X+1 1 0 X+1 1 1 0 X+1 1 0 1 X 1 X 1 0 1 1 X X 1 1 1 X X X X+1 1 0 X 1 0 1 1 0 0 0 1 0
0 0 1 0 0 0 1 1 1 1 X+1 0 0 X+1 X 0 X+1 1 X X+1 0 1 X 1 0 X+1 X+1 0 1 X X 0 X+1 1 1 0 1 X X+1 1 0 X+1 X 0 X 1 0 0 1 X+1 1 X 0 0 X X X+1 X 1 X+1 1 X+1 X+1 1 X+1 0
0 0 0 1 0 1 1 0 1 X X+1 1 0 1 1 X X X X+1 1 1 X+1 X X 0 1 0 0 0 X+1 1 X+1 1 1 X+1 1 0 0 X 0 1 1 1 X X 0 X+1 X+1 1 1 X+1 1 0 X+1 X+1 1 1 X 1 X+1 1 X 1 X+1 X 0
0 0 0 0 1 1 0 1 X+1 X X+1 X+1 1 X 0 1 1 0 X+1 1 X+1 1 X 0 0 X+1 1 1 X 0 1 0 X X X X+1 1 X+1 0 X+1 X+1 0 X 0 X X 1 1 X+1 0 1 1 X+1 1 1 1 X X 0 0 X+1 X X+1 0 1 0
0 0 0 0 0 X 0 0 X 0 X X X X 0 X 0 X 0 0 0 0 X X X X X X 0 0 0 X 0 X X 0 X 0 X 0 0 0 X 0 X X X 0 0 0 X X 0 0 0 0 0 0 X 0 0 0 X X 0 0
0 0 0 0 0 0 X 0 0 0 0 0 X 0 0 X X X X 0 0 X 0 0 X X 0 0 X 0 X 0 X X X 0 0 X 0 X X X X X X X 0 0 0 X 0 X X X 0 0 0 0 0 0 0 X 0 0 0 0
0 0 0 0 0 0 0 X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 X X X X X X X X X X X X X X 0 X X 0 X 0 0 0 X 0 0 X X X X X X X X X 0 X X 0
generates a code of length 66 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+48x^54+88x^55+227x^56+248x^57+261x^58+342x^59+382x^60+408x^61+455x^62+468x^63+462x^64+550x^65+465x^66+430x^67+459x^68+526x^69+455x^70+382x^71+331x^72+322x^73+289x^74+176x^75+158x^76+114x^77+61x^78+30x^79+19x^80+8x^81+9x^82+4x^83+9x^84+4x^86+1x^102
The gray image is a linear code over GF(2) with n=132, k=13 and d=54.
This code was found by Heurico 1.16 in 9.89 seconds.