The generator matrix

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

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+166x^63+353x^64+382x^65+421x^66+362x^67+381x^68+340x^69+293x^70+336x^71+270x^72+252x^73+110x^74+102x^75+123x^76+78x^77+65x^78+22x^79+22x^80+2x^81+3x^82+4x^83+2x^84+2x^85+4x^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 22.9 seconds.