The generator matrix

 1  0  0  0  1  1  1  0  0 X^2 X^2  1  1  1  1  1  0 X^2  1  X  1  1 X^2+X  1  0  X  1  1  1 X^2  1 X^2+X  X  1  X  1 X^2+X  X  1 X^2+X X^2+X  1  X  1 X^2  1  1  0  1  X  X  1  0 X^2  1  1 X^2  X  1 X^2  1  0 X^2  1  1  1  1  1  1
 0  1  0  0  0 X^2 X^2 X^2  1  1  1  1 X+1 X^2+1  1 X^2  1  1 X^2+1 X^2+X  0 X^2+X+1  X  X  X  1 X+1 X+1 X^2 X^2+X  X X^2+X  1  0  X  0  1  1 X^2+X  1  1 X^2+1  1  1  X  X X^2+X+1  1 X^2+1  X X^2 X^2+X  1  1  X X+1  1  0 X^2+1  0 X^2+X  X  1 X+1 X^2+X X+1  0 X^2+1 X^2
 0  0  1  0 X^2  1 X^2+1  1 X+1  0 X+1 X^2+X+1  X X^2+X X^2+1 X^2+X  X X^2+X+1  1  X X^2+X X^2  1 X^2+X+1  1  1 X+1 X^2+X X^2+X+1 X^2 X^2  1 X^2+X+1  1  1 X^2+X+1  0  X X^2+X X^2+X X^2+X+1 X+1 X^2+X  1  1 X+1  0 X^2+1  0 X^2 X^2 X^2 X^2  1  1 X^2+1  1  X  X  1 X+1  1 X^2+X  0 X^2  0  X  0  X
 0  0  0  1 X^2+X+1 X^2+X+1  0 X+1 X^2  1 X^2+1 X^2+1 X^2+1  0 X^2  X X^2+X+1 X^2+X+1 X+1  1 X+1 X^2+1  X  0 X^2+X+1 X^2+X X^2+X  0 X+1  1 X^2 X^2 X^2+X+1 X^2+1 X+1 X^2+X X^2 X+1 X^2+1  X X^2+X X^2+X+1  1  X  0 X+1  X  1 X^2+X+1  1  1 X^2+X X^2+X X^2 X^2+1 X^2+X X^2+X  1 X^2+X  X X^2+X X^2+X X+1  0  0 X+1  0  X  0

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 63.

Homogenous weight enumerator: w(x)=1x^0+138x^63+378x^64+386x^65+437x^66+338x^67+429x^68+362x^69+270x^70+282x^71+268x^72+152x^73+191x^74+144x^75+121x^76+90x^77+49x^78+24x^79+23x^80+2x^81+4x^82+2x^83+4x^84+1x^86

The gray image is a linear code over GF(2) with n=276, k=12 and d=126.
This code was found by Heurico 1.16 in 0.737 seconds.