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^2  X  X
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2  0 X^3 X^2 X^2 X^3 X^2 X^3 X^2 X^2  0 X^3+X^2 X^3  0 X^3 X^2 X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^3 X^3  0 X^2 X^3+X^2  0 X^3 X^2 X^3 X^3  0 X^3 X^3+X^2 X^2  0
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0  0 X^3+X^2 X^2  0 X^3 X^2  0 X^3+X^2 X^3  0 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^2 X^2 X^3 X^3  0 X^3+X^2 X^3 X^2  0 X^2 X^3+X^2
 0  0  0 X^3  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0
 0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3  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+114x^48+224x^50+256x^51+392x^52+36x^56+1x^96

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 0.11 seconds.