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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+43x^48+80x^49+84x^50+608x^51+84x^52+80x^53+43x^54+1x^102

The gray image is a linear code over GF(2) with n=408, k=10 and d=192.
This code was found by Heurico 1.16 in 0.062 seconds.