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 X 1 1 X X 1 1 1 1 0 X 1 X 1 1 1 0 1 1 0 1 X 1 X 1 1 X 1 1 X 1 X 1 1 X 1 X X 1 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 1 0 X+1 0 X X+1 1 0 X 1 1 0 1 X X 1 1 X+1 X+1 1 0 X X+1 0 X X 0 X+1 1 1 0 0 X 1 1 X+1 0 1 X+1 1
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 1 X+1 1 1 0 X 0 1 1 X+1 X 1 X+1 1 X 0 X+1 0 X X X+1 1 1 1 X+1 0 X 1 1 X X X+1 X X+1 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 0 1 0 1 0 1 0 0 X+1 1 0 X+1 0 0 X 1 1 1 0 X+1 1 1 0 1 1 X+1 X X X+1 X 0 X+1 X 1 0 1 1 1 0 X+1
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 1 X+1 1 X 1 X 1 1 X X X+1 X+1 0 X+1 1 X X+1 0 0 0 1 X+1 X+1 X+1 X X X+1 0 0 X+1 0 1 X 0 0 X+1 0 1 X+1 X
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 X 0 X X 0 X 0 X 0 0 X X X 0 0 X 0 0 0 0 X X 0 0 X X 0 X X X 0 X 0 X 0 X
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 0 X 0 X X 0 0 X 0 0 X 0 X X 0 0 X X 0 X X X X 0 0 X 0 0 X X X X X 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 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 0 X X X X X X X X X X X X 0 0 X X 0 0 0 0
generates a code of length 65 over Z2[X]/(X^2) who´s minimum homogenous weight is 54.
Homogenous weight enumerator: w(x)=1x^0+163x^54+481x^56+753x^58+868x^60+883x^62+908x^64+1037x^66+1011x^68+821x^70+599x^72+356x^74+190x^76+77x^78+35x^80+5x^82+3x^84+1x^90
The gray image is a linear code over GF(2) with n=130, k=13 and d=54.
This code was found by Heurico 1.16 in 9.6 seconds.