The generator matrix

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

generates a code of length 51 over Z2[X]/(X^4) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+33x^50+70x^51+6x^52+8x^53+2x^54+1x^56+5x^58+2x^59

The gray image is a linear code over GF(2) with n=408, k=7 and d=200.
This code was found by Heurico 1.16 in 0.063 seconds.