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

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+71x^48+120x^50+640x^51+135x^52+40x^54+16x^56+1x^100

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 0.141 seconds.