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

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+17x^48+28x^49+30x^50+104x^51+672x^52+96x^53+31x^54+24x^55+14x^56+4x^57+2x^58+1x^102

The gray image is a linear code over GF(2) with n=416, k=10 and d=192.
This code was found by Heurico 1.16 in 0.094 seconds.