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  X  1  1  1  1  1
 0  X  0  0  X  X a*X a^2*X a^4*X a^5*X a^5*X  X a^5*X a^6*X  0 a*X a^5*X a*X a^5*X a^6*X a^6*X a^2*X  0 a*X a*X a^3*X a^4*X a^5*X a^5*X  X  X  X a*X a^6*X a^6*X  0  0 a^3*X a^6*X a*X a^4*X  0 a^5*X a^2*X  X  0 a*X  X  0  X
 0  0  X  0 a^6*X a^5*X a*X a^6*X a^6*X a*X a^6*X a^2*X a*X a^3*X  X a^5*X a^3*X a^4*X a^4*X  X a^4*X  0 a*X  X a*X a^6*X  0 a^3*X  X a^4*X a*X a^2*X a^6*X a*X a^2*X a^6*X  X  X a^2*X  0 a^3*X a^5*X  X  0 a^6*X  0  X a*X a^5*X a^6*X
 0  0  0  X  X a^4*X a^4*X  X a^6*X a^4*X a^6*X a^6*X a^3*X a*X a^4*X a*X  0  0 a^6*X a^5*X a^6*X a^5*X  X a^5*X  X  X a^5*X a*X a^6*X  0 a^2*X a^4*X a^3*X a^4*X a^5*X a^6*X a^5*X a^4*X a^4*X  0 a^3*X a^6*X  X a^2*X a^5*X a^3*X a*X a^3*X a^4*X  0

generates a code of length 50 over F8[X]/(X^2) who´s minimum homogenous weight is 320.

Homogenous weight enumerator: w(x)=1x^0+84x^320+595x^328+812x^336+3584x^343+623x^344+25088x^351+483x^352+553x^360+420x^368+217x^376+210x^384+84x^392+14x^400

The gray image is a linear code over GF(8) with n=400, k=5 and d=320.
This code was found by Heurico 1.16 in 0.504 seconds.