The generator matrix

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

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+63x^56+8x^57+214x^58+56x^59+450x^60+176x^61+716x^62+336x^63+1053x^64+448x^65+1251x^66+448x^67+1012x^68+336x^69+687x^70+176x^71+400x^72+56x^73+169x^74+8x^75+71x^76+26x^78+10x^80+5x^82+10x^84+3x^86+1x^88+1x^90+1x^92

The gray image is a linear code over GF(2) with n=264, k=13 and d=112.
This code was found by Heurico 1.16 in 4.26 seconds.