The generator matrix

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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+177x^56+40x^57+380x^58+344x^59+694x^60+776x^61+932x^62+1224x^63+1347x^64+1704x^65+1238x^66+1688x^67+1331x^68+1288x^69+936x^70+792x^71+577x^72+272x^73+312x^74+48x^75+161x^76+16x^77+36x^78+55x^80+6x^82+5x^84+2x^88+1x^92+1x^96

The gray image is a linear code over GF(2) with n=264, k=14 and d=112.
This code was found by Heurico 1.16 in 16.2 seconds.