The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+40x^57+6x^58+8x^59+6x^60+2x^62+1x^64

The gray image is a linear code over GF(2) with n=228, k=6 and d=114.
As d=114 is an upper bound for linear (228,6,2)-codes, this code is optimal over Z2[X]/(X^3) for dimension 6.
This code was found by Heurico 1.11 in 0.11 seconds.