The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+50x^49+105x^50+12x^51+10x^52+24x^53+38x^54+4x^55+5x^56+6x^57+1x^58

The gray image is a linear code over GF(2) with n=408, k=8 and d=196.
This code was found by Heurico 1.16 in 0.172 seconds.