The generator matrix

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

generates a code of length 53 over Z2[X]/(X^3) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+84x^48+174x^49+302x^50+234x^51+297x^52+188x^53+179x^54+144x^55+114x^56+90x^57+70x^58+22x^59+77x^60+28x^61+23x^62+16x^63+3x^64+2x^66

The gray image is a linear code over GF(2) with n=212, k=11 and d=96.
This code was found by Heurico 1.16 in 0.183 seconds.