The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1 X^2+X  1  1  1  0  1  1 X^2+X X^2+X  1  1  0  1  X  1  1  1  1  1  1  1  1 X^2  1  1  1  1  0  1  1  1  0  1  1  1  1  1  1  1  1  1  1  X
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X  1 X^2+1  0 X+1  1 X^2+X X^2+1  1  1  0 X+1  1 X^2+X  1 X^2+X+1  0 X^2+1 X^2+1  1 X^2+1  X X+1  1 X+1 X+1 X^2 X^2+1  1 X^2+X+1  0 X^2+1  1  1  1 X^2+1 X^2+X+1 X+1 X^2+X+1 X+1 X^2+X+1 X+1 X+1  X
 0  0 X^2  0  0  0  0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2  0  0
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2  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  0 X^2  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0  0  0  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 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+350x^48+224x^50+496x^52+256x^54+592x^56+32x^58+80x^60+15x^64+2x^80

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 0.263 seconds.