The generator matrix

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

generates a code of length 69 over Z2[X]/(X^3) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+117x^62+104x^63+392x^64+228x^65+434x^66+312x^67+430x^68+268x^69+377x^70+264x^71+383x^72+268x^73+213x^74+88x^75+100x^76+4x^77+46x^78+27x^80+25x^82+8x^84+4x^86+1x^88+2x^92

The gray image is a linear code over GF(2) with n=276, k=12 and d=124.
This code was found by Heurico 1.16 in 1.1 seconds.