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  X  0  X  1  0  1  X X^2  X  1  1  X  0 X^2  X  1  0  0  1  1  0  1  1  X  1  0  0  1  X  1  X  1  1  X  1  1  X  1  1  X  X
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  0 X^2+X X^2 X^2+X X^2 X^2+X  X  X  X  X  0  0 X^2+X  X X^2  0 X^2 X^2+X  X  X X^2+X  X X^2  X  X  X  X  X  X  X X^2 X^2+X  X X^2+X X^2  X  X  0 X^2  0  0  0 X^2+X X^2+X X^2+X  X  X  X  X X^2 X^2 X^2 X^2
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X  0  X X^2  X X^2  0 X^2+X  0  X X^2+X X^2  X X^2 X^2+X X^2  0  X  0  X X^2 X^2+X  X  0 X^2 X^2+X  X  0 X^2+X  X  0  0 X^2+X  0 X^2  0  0 X^2+X X^2+X  0  X  X X^2+X  X  0 X^2 X^2 X^2+X  0  X X^2+X  0 X^2 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  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 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2  0  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 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  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0
 0  0  0  0  0  0 X^2  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  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0 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 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  0  0  0  0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  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 53.

Homogenous weight enumerator: w(x)=1x^0+20x^53+108x^54+96x^55+178x^56+188x^57+363x^58+286x^59+738x^60+412x^61+1491x^62+486x^63+2055x^64+524x^65+2421x^66+568x^67+2239x^68+548x^69+1376x^70+420x^71+679x^72+268x^73+282x^74+166x^75+192x^76+76x^77+75x^78+22x^79+46x^80+12x^81+21x^82+4x^83+15x^84+6x^86+1x^88+1x^90

The gray image is a linear code over GF(2) with n=264, k=14 and d=106.
This code was found by Heurico 1.16 in 95.4 seconds.