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  X  X  1 X^3  X  X  1  1  1  X
 0  X  0 X^3+X^2+X X^3 X^2+X  0  X X^2 X^3+X^2+X X^2  X X^3+X^2 X^3+X X^2 X^3+X^2+X X^2+X X^3 X^3+X^2 X^3+X^2+X X^3+X^2  X X^3+X^2+X X^3+X^2 X^2 X^3+X^2+X  0  X X^3+X^2 X^3+X X^3  0 X^3+X^2 X^2+X X^2+X X^3+X^2+X X^3+X^2 X^3+X X^3+X X^3  0 X^3+X^2 X^2+X X^3+X^2 X^3  X X^3+X^2+X X^2  0  0  0 X^3+X^2+X
 0  0 X^3+X^2  0  0 X^3+X^2 X^2 X^2 X^2 X^3+X^2 X^2 X^3+X^2  0 X^3 X^3  0  0 X^3 X^3+X^2 X^3 X^2 X^2 X^2  0 X^2 X^3 X^3  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^2 X^3  0 X^3+X^2 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3 X^3+X^2  0  0 X^2 X^3+X^2
 0  0  0 X^3+X^2 X^2 X^3+X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^3 X^2 X^3+X^2 X^2 X^3 X^3 X^2 X^3 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2  0  0 X^2 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^3  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+186x^48+64x^49+190x^50+336x^51+565x^52+312x^53+156x^54+40x^55+145x^56+8x^57+22x^58+8x^59+14x^60+1x^92

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 9.34 seconds.