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 X^2  X  0  1  1  X  1  1  1  X  1  1  X  X  1  1  1  1  1  X  1  X X^2  X  0  1  1  1  X  1  X X^2  X  1
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X  X  X  X X^2 X^2+X  X X^2  0 X^2+X X^2 X^2  0  X  X  X  0  0  X  X  X  X X^2+X X^2+X  0  X X^2 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  0  X X^2+X  0 X^2 X^2+X  0 X^2 X^2 X^2+X  X X^2  0  0 X^2 X^2 X^2  X X^2+X  X
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2+X X^2  0  X X^2  0  0  X X^2  X  X  0  X X^2 X^2+X  0 X^2 X^2+X X^2  0 X^2 X^2+X  0 X^2+X  0 X^2  X  X  X  0 X^2  X X^2+X  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0 X^2  X  X  0  X X^2 X^2
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X X^2  X  0  X X^2+X  X  X X^2 X^2  0 X^2+X X^2 X^2  0  X  0 X^2+X X^2+X X^2+X X^2+X  X X^2+X X^2+X X^2+X  0 X^2+X X^2 X^2+X X^2 X^2+X X^2+X X^2+X X^2  0  X  0  0 X^2+X  0  X  X X^2+X X^2 X^2+X X^2+X  X  0  X X^2 X^2  0 X^2
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X X^2+X  X  X X^2 X^2+X  X X^2 X^2+X  X  0  0 X^2 X^2  0 X^2+X  0 X^2+X  0  0  X  X  X  X X^2  0  X  0 X^2 X^2  X  0 X^2 X^2  X X^2  0  0 X^2+X  0 X^2 X^2 X^2+X  X  0  X X^2+X  0 X^2+X X^2+X X^2+X X^2+X
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  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  0  0  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 58.

Homogenous weight enumerator: w(x)=1x^0+146x^58+4x^59+386x^60+56x^61+374x^62+192x^63+450x^64+260x^65+478x^66+260x^67+497x^68+192x^69+260x^70+56x^71+212x^72+4x^73+114x^74+100x^76+30x^78+17x^80+6x^82+1x^100

The gray image is a linear code over GF(2) with n=264, k=12 and d=116.
This code was found by Heurico 1.16 in 1.53 seconds.