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^2  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X X^3  X X^3+X^2 X^3+X^2+X  X  0 X^3+X^2 X^3+X^2+X X^3+X^2+X X^3 X^2 X^3+X X^3+X  0 X^3+X^2+X  0 X^3+X^2+X X^3+X^2 X^3+X^2 X^3+X X^3+X X^3 X^3 X^2 X^2+X X^2 X^2+X X^3+X^2+X X^2  0 X^3 X^2+X X^3+X^2 X^2+X X^3+X X^3+X^2+X X^3+X^2 X^3+X^2  0
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0  0 X^2 X^3 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 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3  0  0  0 X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^2 X^3  0 X^3  0
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0  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+35x^48+232x^49+27x^50+448x^51+28x^52+208x^53+36x^54+8x^57+1x^98

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 0.157 seconds.