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

generates a code of length 52 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+290x^48+1472x^52+280x^56+4x^64+1x^96

The gray image is a linear code over GF(2) with n=416, k=11 and d=192.
This code was found by Heurico 1.16 in 1.19 seconds.