The generator matrix

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

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+48x^45+151x^46+222x^47+285x^48+342x^49+423x^50+434x^51+367x^52+420x^53+454x^54+322x^55+204x^56+194x^57+104x^58+46x^59+28x^60+10x^61+17x^62+6x^64+8x^65+1x^66+5x^68+2x^69+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 51.7 seconds.