The generator matrix

 1  0  0  0  0  0  0  1  1  1  0  1  X  1  1  0  1  0  X  X  1  1  1  1  1  1  1  0  X  X  1  0  0  X  0  0  1  1  1  0  X  1  X  0  X  1  1  1  1  0  0  0  1  0  X  1  1  1  X  X  0  0  1  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  1  1  1  1 X+1 X+1 X+1  1  1 X+1  0  1  1  X  1  1  1  X  1 X+1  X  X  0  X  0  1  X  0 X+1  X  X  X  1  X  1  0  1  1  0  1 X+1  1  1  1  1  0  0  X  0
 0  0  1  0  0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  0  0  X  X  X  X  X  X  0  X  0  X  0  0  X X+1 X+1  1  1  1  1 X+1 X+1  1  1  1 X+1 X+1  1 X+1  1  1 X+1  1  1 X+1  1  1 X+1 X+1  0  X  1 X+1  X  0
 0  0  0  1  0  0  0  0  0  X  X  1  1 X+1 X+1  1  1  1 X+1  X  X  1 X+1  X  X  1 X+1  1 X+1  X  0 X+1  X  0  X X+1  X  1  X X+1  1  0  X  0  1  0  1  X X+1  X X+1 X+1  0 X+1  0  X  X X+1  0 X+1  1  0 X+1  1  0  1
 0  0  0  0  1  0  0  X  1 X+1  1  0  1  1  1 X+1  X X+1  0  0  X  X  0  X  1  1  1  0  X X+1  0 X+1  1  0  X  X X+1  1  X  X  1 X+1 X+1 X+1 X+1  X  1  1 X+1 X+1 X+1  0  0  X  X  0  X X+1  X  1  0  X  0  0 X+1  0
 0  0  0  0  0  1  0 X+1  1  0  1  X X+1 X+1  0  X X+1  1 X+1  1 X+1  1  X  X  0  1  0 X+1  X  1 X+1 X+1  X  0  X X+1  1  0  0  1  X  0 X+1  1 X+1  0 X+1  1 X+1 X+1  0 X+1  1  1  1  1  X X+1  X  1  X X+1 X+1  X  0  0
 0  0  0  0  0  0  1  1  X  1  1 X+1  X  1  X  1  X X+1  X X+1  X X+1  0  1  X  0 X+1  1 X+1  0  1  1 X+1  X  1  0  X  1 X+1  X  0  X X+1  X  1  X  0 X+1  0 X+1 X+1  0 X+1 X+1 X+1  0  X  1 X+1  1  0  0  0  1  0  X

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+256x^54+705x^56+1044x^58+1489x^60+1702x^62+2056x^64+1964x^66+1955x^68+1848x^70+1353x^72+1086x^74+544x^76+280x^78+85x^80+10x^82+3x^84+2x^86+1x^108

The gray image is a linear code over GF(2) with n=132, k=14 and d=54.
This code was found by Heurico 1.16 in 87.7 seconds.