The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  1  0  1  1 X^2+X  1  1  1  0  1 X^2+X  1  1  1 X^2  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  0  0 X^2  X  X  X  1  1  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+1  1 X^2+X X^2+X  0 X+1  1  0 X^2+1  1 X^2+X X+1  X  1 X^2+1  1  0 X^2+X+1 X^2  1 X^2+1  1 X^2+X  0 X^2 X^2+X X^2+X  X  X X^2  0 X^2  0 X+1 X^2+1  X  X  1  1 X^2+X  X  1 X^2+1  0
 0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0  0  0 X^2  0  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2  0  0  0  0  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0 X^2 X^2  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+72x^48+100x^49+96x^50+104x^51+104x^52+124x^53+72x^54+80x^55+95x^56+92x^57+56x^58+8x^59+11x^60+4x^61+2x^64+1x^68+1x^72+1x^88

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 0.0981 seconds.