The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1 X^2  1  1  1  1  1  X  1 X^2  X
 0  X  0  X  0  0  X X^2+X X^2 X^2  X X^2+X X^2  X  X  0  X X^2  0 X^2+X X^2+X  0  0  X  0 X^2 X^2  0  X X^2+X X^2+X  X  0  X  0  X X^2 X^2+X X^2 X^2+X  X  X  X  X X^2+X  X X^2+X X^2+X X^2+X  X  X  X X^2
 0  0  X  X  0 X^2+X  X X^2  0  X  X  0  X X^2+X  0 X^2  X X^2+X X^2  0  X X^2+X X^2  0  0 X^2  X X^2+X  X  0 X^2+X X^2  0  X X^2 X^2+X X^2 X^2+X  0  0 X^2  X X^2 X^2+X  X X^2  0  0 X^2  X  0 X^2+X X^2
 0  0  0 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0  0  0  0
 0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0  0  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+144x^48+52x^50+128x^51+68x^52+256x^53+32x^54+128x^55+136x^56+40x^58+28x^60+6x^64+4x^66+1x^96

The gray image is a linear code over GF(2) with n=212, k=10 and d=96.
This code was found by Heurico 1.16 in 0.363 seconds.