The generator matrix

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

generates a code of length 57 over Z2[X]/(X^3) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+92x^51+260x^52+466x^53+410x^54+396x^55+352x^56+406x^57+369x^58+362x^59+248x^60+238x^61+152x^62+128x^63+59x^64+68x^65+53x^66+14x^67+16x^68+4x^69+2x^73

The gray image is a linear code over GF(2) with n=228, k=12 and d=102.
This code was found by Heurico 1.16 in 0.568 seconds.