The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^3  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  X  1  1  X  1  1  0  1  1  X  1  1 X^3+X^2  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2 X^2+X  0 X^2+X X^3 X^3+X X^2  X X^2+X  X  0 X^2+X X^3+X^2 X^3+X X^3+X^2+X X^3  0  X X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3+X^2+X  0 X^3  X  X  X X^3+X^2 X^2 X^3+X X^3+X^2+X  X  0  X X^3+X^2+X X^2+X X^2+X X^3+X^2+X X^3+X  X X^2+X  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3+X^2  0  0 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^3  0  0 X^3 X^3+X^2 X^2 X^2 X^3+X^2  0 X^3+X^2 X^2 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3  0 X^3+X^2 X^2  0 X^3+X^2  0 X^3  0  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0  0  0  0 X^3
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3

generates a code of length 53 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+24x^48+124x^49+147x^50+186x^51+429x^52+330x^53+403x^54+144x^55+100x^56+52x^57+19x^58+54x^59+21x^60+6x^61+6x^62+1x^64+1x^86

The gray image is a linear code over GF(2) with n=424, k=11 and d=192.
This code was found by Heurico 1.16 in 0.219 seconds.