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

generates a code of length 64 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+43x^54+155x^56+302x^58+452x^60+698x^62+861x^64+687x^66+426x^68+265x^70+125x^72+28x^74+16x^76+16x^78+9x^80+7x^82+2x^84+2x^86+1x^96

The gray image is a linear code over GF(2) with n=256, k=12 and d=108.
This code was found by Heurico 1.16 in 1.54 seconds.