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

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+152x^48+40x^50+632x^52+512x^53+464x^54+164x^56+8x^58+72x^60+2x^64+1x^96

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 0.296 seconds.