The generator matrix

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

generates a code of length 52 over Z2[X]/(X^3) who´s minimum homogenous weight is 45.

Homogenous weight enumerator: w(x)=1x^0+32x^45+135x^46+236x^47+290x^48+388x^49+389x^50+398x^51+487x^52+382x^53+348x^54+366x^55+245x^56+182x^57+101x^58+28x^59+22x^60+18x^61+17x^62+10x^63+10x^64+6x^65+2x^67+1x^68+2x^70

The gray image is a linear code over GF(2) with n=208, k=12 and d=90.
This code was found by Heurico 1.16 in 0.69 seconds.