The generator matrix

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

generates a code of length 66 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+46x^54+94x^55+214x^56+246x^57+387x^58+504x^59+537x^60+778x^61+875x^62+1148x^63+1262x^64+1320x^65+1556x^66+1384x^67+1346x^68+1188x^69+843x^70+690x^71+536x^72+462x^73+279x^74+236x^75+161x^76+98x^77+90x^78+36x^79+35x^80+4x^81+18x^82+4x^83+4x^84+1x^86+1x^94

The gray image is a linear code over GF(2) with n=264, k=14 and d=108.
This code was found by Heurico 1.16 in 20.8 seconds.